mm-1499 === Subject: Re: Existence of countable Hamel basis by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHDJ5P23976; >>All normed spaces as vector spaces have basis,so called >>Hamel basis. >>Hamel bases in infinite dimensional Banach spaces >>are uncountable.This follows from Baire category theorem. >>What if the infinite dimensional space isn't complete? >>Does it always contain countable Hamel basis? >Of course not; it might, for instance, contain a complete >infinite dimensional subspace even though it itself isn't >complete. === Subject: Re: Existence of countable Hamel basis at 09:34 PM, anonymous@mathforum.org (Felix) said: >All normed spaces as vector spaces have basis,so called >Hamel basis. >Hamel bases in infinite dimensional Banach spaces >are uncountable.This follows from Baire category theorem. What if the >infinite dimensional space isn't complete? >Does it always contain countable Hamel basis? No. >The space d={(x_n):only finitely many x_n =/=0} has >e_n=(0,..,0,1,0,...0) as Hamel basis. Make a slight change; index the elements on an uncountable set. That is, instead of {x in R^I| all but finitely many X_i are zero} use {x in R^U, U uncountable| all but finitely many X_i are zero}. That gives you an example of an incomplete space with no countable Hamel basis. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Existence of countable Hamel basis >All normed spaces as vector spaces have basis,so called >Hamel basis. >Hamel bases in infinite dimensional Banach spaces >are uncountable.This follows from Baire category theorem. >What if the infinite dimensional space isn't complete? >Does it always contain countable Hamel basis? >>Of course not; it might, for instance, contain a complete >>infinite dimensional subspace even though it itself isn't >>complete. Yes. Don't waste your time thinking about subtleties; consider appropriate direct sums of two suitable spaces. Lee Rudolph === Subject: Re: Counting set covers by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHDOgn24792; >Hello all. I was wondering if there is some relatively simple way >to count the number of set covers of a set of size n that satisfy >the following properties: >1. No set in the cover is a subset of another set in the cover >2. For all sets A(i) in the cover: > A(i) (union of all A(k) (k != i)) = {} >> S = /_j A_j >> nulset = A_k - (/_j A_j - A_k) = A_k - SA_k = A_k >Unfortunately (/_j A_j - A_k) != SA_k. Actually, the problem is that /_{j != k} A_j != /_j A_j - A_k. Consider the cover {{1, 2}, {2, >3}, {1, 3}} of {1, 2, 3}. It satisfies the above two properties, yet >none of the sets are empty. It is incidentally the only such cover of >{1, 2, 3} besides {{1, 2, 3}}. It looks like {{1, 2, 3}} doesn't satisfy the second condition, since the union of an empty collection is empty and this would force {1, 2, 3} to be included in the empty set. Todd Trimble === Subject: Re: Counting set covers >>Hello all. I was wondering if there is some relatively simple way >>to count the number of set covers of a set of size n that satisfy >>the following properties: >>1. No set in the cover is a subset of another set in the cover >>2. For all sets A(i) in the cover: >> A(i) (union of all A(k) (k != i)) = {} >S = /_j A_j >nulset = A_k - (/_j A_j - A_k) = A_k - SA_k = A_k >>Unfortunately (/_j A_j - A_k) != SA_k. > Actually, the problem is that > /_{j != k} A_j != /_j A_j - A_k. > Consider the cover {{1, 2}, {2, >>3}, {1, 3}} of {1, 2, 3}. It satisfies the above two properties, yet >>none of the sets are empty. It is incidentally the only such cover of >>{1, 2, 3} besides {{1, 2, 3}}. > It looks like {{1, 2, 3}} doesn't satisfy the second condition, > since the union of an empty collection is empty and this would > force {1, 2, 3} to be included in the empty set. Ah, yes. I meant to include 'the set of the set' into the count as well, so I should have mentioned that. But, the problem is largely the same anyway. -- Daniel Sj.9ablom === Subject: Re: Counting set covers by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHDOgC24796; === >Subject: Counting set covers >> Hello all. I was wondering if there is some relatively simple way >> to count the number of set covers of a set of size n that satisfy >> the following properties: >> 1. No set in the cover is a subset of another set in the cover >> 2. For all sets A(i) in the cover: >> A(i) (union of all A(k) (k != i)) = {} >S = /_j A_j >nulset = A_k - (/_j A_j - A_k) = A_k - SA_k = A_k >> The second property could also be formulated as: There is no set in >> the cover that contains an element not contained in another set in >> the cover. >A_k subset /_j A_j - A_k = SA_k. Thus again A_k = nulset. >The second property requires all A_k to be empty. >> There are still a huge amount of such covers, but I would be >> interested in comparing the amount of such covers to the amount of >> all possible set covers. >There are none unless the set S being covered is empty. Nonsense. For S = {1, 2, 3}, the cover { {1, 2}, {1, 3}, {2, 3} } meets the OP's conditions. Todd Trimble === Subject: Geometry software Hi! I am looking for a software that letĒs you draw geometric figures and that the software calculates lengths and ratios. Do you know of such a software? Must be many but you probably have more experience than me. === Subject: Re: Geometry software > Hi! I am looking for a software that letĒs you draw geometric figures and > that the software calculates lengths and ratios. Do you know of such a > software? Must be many but you probably have more experience than me. A commercial software popular with educators is Geometer's Sketchpad. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Geometry software Hi! I am looking for a software that letĒs you draw geometric figures and that the software calculates lengths and ratios. Do you know of such a software? Must be many but you probably have more experience than me. === Subject: Re: Geometry software > Hi! I am looking for a software that let.8bs you draw geometric figures and > that the software calculates lengths and ratios. Do you know of such a > software? Must be many but you probably have more experience than me. http://www.euclidraw.com/ -- I. N. G. --- http://users.forthnet.gr/ath/jgal/ === Subject: Lebesgue measurable functions I need to see an example of a Lebesgue measurable function f: R -->R such that inverse image of a Lebesgue measurable set is not Lebesgue measurable. Examples through cardinality argument will be accepted. === Subject: Re: Lebesgue measurable functions > I need to see an example of a Lebesgue measurable function f: R -->R such > that inverse image of a Lebesgue measurable set is not Lebesgue measurable. > Examples through cardinality argument will be accepted. Can you find a Lebesgue measurable f that maps [0,1] bijectively to the Cantor set? Every subset of the Cantor set is Lebesgue measurable, but not every subset of [0,1] is. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Lebesgue measurable functions > I need to see an example of a Lebesgue measurable function f: R -->R such > that inverse image of a Lebesgue measurable set is not Lebesgue measurable. > Examples through cardinality argument will be accepted. > Can you find a Lebesgue measurable f that maps [0,1] bijectively to the > Cantor set? Every subset of the Cantor set is Lebesgue measurable, but > not every subset of [0,1] is. > -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ There is also a continuous (strictly increasing) bijection of [0,1] onto [0,2] which maps the Cator set (of Lebesgue measure 0) onto a Cantor-like set of Lebesgue measure 1. It appeared recently: x+C(x) where C is the Cantor function. === Subject: Re: Lebesgue measurable functions > I need to see an example of a Lebesgue measurable function f: R -->R such > that inverse image of a Lebesgue measurable set is not Lebesgue measurable. > Examples through cardinality argument will be accepted. > > Can you find a Lebesgue measurable f that maps [0,1] bijectively to the > Cantor set? Every subset of the Cantor set is Lebesgue measurable, but > not every subset of [0,1] is. > -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ > There is also a continuous (strictly increasing) bijection of [0,1] onto > [0,2] which maps the Cator set (of Lebesgue measure 0) onto a Cantor-like > set of Lebesgue measure 1. It appeared recently: x+C(x) where C is the > Cantor function. Cator set is of course my private nickname for the Cantor set. (Sitting in my office on Saturday night, ready to answer questions from students writing a final exam...) === Subject: Convexity (x^2+y^2)^a + (x*y)^2 <= 1 What is the minimal a for which the set consisted of the solutions of the above inequality is convex? How to solve this and similar problems? Niles W. === Subject: Re: Convexity > (x^2+y^2)^a + (x*y)^2 <= 1 > What is the minimal a for which the set consisted of the solutions of > the above inequality is convex? Is the question unclear/incorrect or the answer trivial? Niles W. === Subject: Re: Convexity > (x^2+y^2)^a + (x*y)^2 <= 1 > What is the minimal a for which the set consisted of the solutions of > the above inequality is convex? > Is the question unclear/incorrect or the answer trivial? None of the above, I think. It's just hard. I'll leave consideration of a <= 0 to you, and suppose a > 0. By symmetry it's enough to consider the first quadrant, where we can take y as a function of x for 0 <= x <= 1, y(0) = 1 and y(1) = 0. It looks to me like when we decrease a, the first place y'' becomes positive would be where x=y, where (2 x^2)^a + x^4 = 1. I think the answer is the value of a in the solution of the system of equations (2 x^2)^a + x^4 = 1 -a + (a + 2) x^4 = 0 which is approximately 0.21406286037879413377. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: .99999... still=/= 1 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHFa5605219; >> So from another point of view, >> .999... =/= 1 >The locution .999.... is a meaningless string of symbols. It is not a >properly expressed mathematical entity. Whereas: >SUM [n >=1] (9/10^n) >is a proper mathematical expression (it is equal to 1) >So the sentence .999... =/= 1 is meaningless. >You are a troll and a moron. >Bob Kolker Bob, Please avoid the name calling. It gives sci.math a bad reputation. You may not agree with SE's logic (I do not agree with it either), but it is not OK to call him names because of your disagreement with him on things mathmatical. Let's keep it friendly, and on topic. Please, no more name calling. - MO === Subject: Re: .99999... still=/= 1 > So from another point of view, > > .999... =/= 1 >>The locution .999.... is a meaningless string of symbols. It is not a >>properly expressed mathematical entity. Whereas: >>SUM [n >=1] (9/10^n) >>is a proper mathematical expression (it is equal to 1) >>So the sentence .999... =/= 1 is meaningless. >>You are a troll and a moron. >>Bob Kolker >Bob, >Please avoid the name calling. It gives sci.math a bad reputation. >You may not agree with SE's logic (I do not agree with it either), >but it is not OK to call him names because of your disagreement >with him on things mathmatical. >Let's keep it friendly, and on topic. Please, no more name calling. about the math part. >- MO Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > Bob, > Please avoid the name calling. It gives sci.math a bad reputation. > You may not agree with SE's logic (I do not agree with it either), > but it is not OK to call him names because of your disagreement > with him on things mathmatical. > Let's keep it friendly, and on topic. Please, no more name calling. Enterprise has bone told again and again what a series is, what convergence is and what a limit is. He does not seem to learn. That justifies the term moron, a low level intellect. He is also a troll because he repeats his errors again and again. So the appleation is well justified. Bob Kolker === Subject: Re: .99999... still=/= 1 >> Bob, >> Please avoid the name calling. It gives sci.math a bad reputation. >> You may not agree with SE's logic (I do not agree with it either), >> but it is not OK to call him names because of your disagreement >> with him on things mathmatical. >> Let's keep it friendly, and on topic. Please, no more name calling. >Enterprise has bone told again and again what a series is, what >convergence is and what a limit is. He does not seem to learn. That >justifies the term moron, a low level intellect. >He is also a troll because he repeats his errors again and again. >So the appleation is well justified. >Bob Kolker I have been using a non-standard approach to this math problem. And usually the way to expansion to new frontiers in math. is to challenge what is usually accepted as correct but may not necessarily be correct. If it wasn't for Columbus, you people might have fallen off the edge of the earth. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > I have been using a non-standard approach to this math problem. You are full of . You don't know what non-standard arithmetic is andyou would not know a hyperreal number if it bit your nose. Bob Kolker === Subject: Re: .99999... still=/= 1 Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >You may not agree with SE's logic (I do not agree with it either), >but it is not OK to call him names because of your disagreement >with him on things mathmatical. They don't have a disagreement about anything mathematical. It should be clear by now that SE is not arguing in good faith, but is just trolling. -- Richard === Subject: Re: .99999... still=/= 1 >>You may not agree with SE's logic (I do not agree with it either), >>but it is not OK to call him names because of your disagreement >>with him on things mathmatical. >They don't have a disagreement about anything mathematical. It should >be clear by now that SE is not arguing in good faith, but is just >trolling. >-- Richard I sincerely have been debating this topic the best way I perceive it. For crying out loud, do you actually believe a real number equals a number that isn't real? Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 In sci.math, S. Enterprize Company >You may not agree with SE's logic (I do not agree with it either), >but it is not OK to call him names because of your disagreement >with him on things mathmatical. >>They don't have a disagreement about anything mathematical. It should >>be clear by now that SE is not arguing in good faith, but is just >>trolling. >>-- Richard > I sincerely have been debating this topic the best way I > perceive it. For crying out loud, do you actually believe a > real number equals a number that isn't real? Well, here's a fine mess you've gotten us into... :-) First, what is a real number anyway? Despite our many valiant attempts to beat you over the head with the club of reason, it's clear you're resisting -- and it may very well because the club of reason is actually a thin, wispy, non-existent fog of a metaphor. In short, real numbers are about as real as pink elephants. They do not exist. Oh, sure, one can blather on about measuring 1.25 inches or 3 1/2 cups of coffee or an air pressure of 101 kPa during a nice sunny day -- but those are physical measurements, not numbers per se. Try catching a number in a butterfly net -- or any other kind of net, for that matter. One can't do it; the best one might get is a pair of swallowtailed yellowbeaks. Or something. (Or was that yellowtailed swallowbeaks? Does one count an egg as half of a bird, or a third? Well, never mind that; ornithology was never my strongest subject.) The best we can do is lay a groundwork of phantom assumptions, such as Peano's Axioms and Dedekind cuts, but here is where the problems start. First, what does '=' actually mean? For most of us, we simply accept that limits make sense -- but there are far deeper issues here; the partial sums, for example, of the series 1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ... are all rational, but the result is pi^2/6. Hey, waitaminnit, that ain't in Q! What happened? Good question. Or one can try 1 + 1/2 + 1/3 + ... All your partial sums are belong to Q, but the series diverges; this one has no limit, although one might make a case that 1 + 1/2 + 1/3 + ... = +oo. but remember that +oo is not a real number. Of course, the usage of the ellipsis ('...') is a bit tricky. Take, for example, this definition: e = 2.718281828... Now before one asks uh, is that rational? -- turns out this is Euler's Number, which equates to the series e = 1/0! + 1/1! + 1/2! + 1/3! + ... and no, it is not rational (although all of the partial sums are!); a more honest ellipsis might be e = 2.718281828459... So we fall back on convention. You may have heard the expression what I say three times is true. (It's not quite true, admittedly, but never mind that.) So one might write 1/7 = 0.142857142857142857... with the understanding that the last 6 digits repeat endlessly. (It turns out they do; a long-division proof is left to the interested reader, or one can simply multiply 142857*7 = 999999 = 10^6 - 1 and/or note that 1/(1-x) = 1+x+x^2+x^3+... for any x between -1 and +1.) Or 1/11 = 0.090909... or even 1/9 = 0.111... So what does 0.999... really mean? Endless 9's, in this case. A proper treatment of such a number might involve summation of the infinite series sum(i=1,+oo) (9 * 10^(-i)). If numbers are an abstract_1 concept, this sum is an abstract_3 (simple expressions are abstract_2, in some sense). The partial sums of this series are of course sum(i=1,n) (9 * 10^(-i)); a little work with a competent algebra book or symbolic calculator show that a partial sum sum(i=1,n) (9 * 10^(-i)) = 1 - 10^n = 0.999...9. There's that ellipsis again, this time in a different context; the 9's do *not* repeat endlessly in this case (unless one is Gary Denke, but one doesn't really want to know the details there). In this case, there are n 9's total. Of course, I've pointed this out before to you, and so far it's yet to sink in, unlike the iron spike in the case of Phinehas Gage. (ObOuch: Ouch.) Unfortunately, to most calculators, all numbers are rationals -- furthermore, to modern computers, all numbers are multiples of a power of 2, with some fudging on the arithmetic side to make it look otherwise. (The standard representation is r = 2^e * M, where M is up to about 53 bits and e can range from -2048 to +2047 or thereabouts.) Therefore, a partial sum may yield anomalies if not done carefully. For example, to a computer, 1/3 = 0x3fd5555555555555 . This is readily verified using C and a hack such as the following: #include int main() { union { unsigned char c[sizeof(double)]; double d; } u; int i; u.d = 1.0/3.0; printf(1/3 = 0x); for(i=0;i and #if BYTE_ORDER == BIG_ENDIAN in appropriate spots.) The first bit is the sign bit; the next 11 is a modified exponent, and the rest are the mantissa, with a hidden-1. For example, 1.0 = 0x3ff0000000000000 2.0 = 0x4000000000000000 3.0 = 0x4008000000000000 4.0 = 0x4010000000000000 5.0 = 0x4014000000000000 In a very real sense, to a computer 1/3 = 6004799503160661/18014398509481984 = .333333333333333314829616256247390992939472198486328125 . (Note that 15555555555555(16) = 6004799503160661(10).) One can use an infinite-precision calculator such as bc to derive these results: $ bc <In sci.math, S. Enterprize Company > >>You may not agree with SE's logic (I do not agree with it either), >>but it is not OK to call him names because of your disagreement >>with him on things mathmatical. >They don't have a disagreement about anything mathematical. It should >be clear by now that SE is not arguing in good faith, but is just >trolling. >-- Richard >> I sincerely have been debating this topic the best way I >> perceive it. For crying out loud, do you actually believe a >> real number equals a number that isn't real? >Well, here's a fine mess you've gotten us into... :-) >First, what is a real number anyway? Despite our many valiant >attempts to beat you over the head with the club of reason, >it's clear you're resisting -- and it may very well because >the club of reason is actually a thin, wispy, non-existent fog >of a metaphor. >In short, real numbers are about as real as pink elephants. >They do not exist. Oh, sure, one can blather on about >measuring 1.25 inches or 3 1/2 cups of coffee or an >air pressure of 101 kPa during a nice sunny day -- but >those are physical measurements, not numbers per se. >Try catching a number in a butterfly net -- or any other kind >of net, for that matter. One can't do it; the best one might >get is a pair of swallowtailed yellowbeaks. Or something. >(Or was that yellowtailed swallowbeaks? Does one count an >egg as half of a bird, or a third? Well, never mind that; >ornithology was never my strongest subject.) >The best we can do is lay a groundwork of phantom assumptions, >such as Peano's Axioms and Dedekind cuts, but here is where >the problems start. >First, what does '=' actually mean? For most of us, we simply >accept that limits make sense -- but there are far deeper issues >here; the partial sums, for example, of the series >1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ... >are all rational, but the result is pi^2/6. Hey, waitaminnit, that >ain't in Q! What happened? >Good question. >Or one can try >1 + 1/2 + 1/3 + ... >All your partial sums are belong to Q, but the series diverges; >this one has no limit, although one might make a case that >1 + 1/2 + 1/3 + ... = +oo. >but remember that +oo is not a real number. >Of course, the usage of the ellipsis ('...') is a bit tricky. Take, >for example, this definition: >e = 2.718281828... >Now before one asks uh, is that rational? -- turns out this is >Euler's Number, which equates to the series >e = 1/0! + 1/1! + 1/2! + 1/3! + ... >and no, it is not rational (although all of the partial sums are!); >a more honest ellipsis might be >e = 2.718281828459... >So we fall back on convention. You may have heard the expression >what I say three times is true. (It's not quite true, admittedly, >but never mind that.) So one might write >1/7 = 0.142857142857142857... >with the understanding that the last 6 digits repeat endlessly. >(It turns out they do; a long-division proof is left to the >interested reader, or one can simply multiply 142857*7 = 999999 = 10^6 - 1 >and/or note that 1/(1-x) = 1+x+x^2+x^3+... for any x between -1 and +1.) >1/11 = 0.090909... >or even >1/9 = 0.111... >So what does 0.999... really mean? Endless 9's, in this case. >A proper treatment of such a number might involve summation of the >infinite series sum(i=1,+oo) (9 * 10^(-i)). If numbers are >an abstract_1 concept, this sum is an abstract_3 (simple expressions >are abstract_2, in some sense). The partial sums of this series >are of course sum(i=1,n) (9 * 10^(-i)); a little work with a competent >algebra book or symbolic calculator show that a partial sum >sum(i=1,n) (9 * 10^(-i)) = 1 - 10^n = 0.999...9. There's that >ellipsis again, this time in a different context; the 9's do *not* >repeat endlessly in this case (unless one is Gary Denke, but one >doesn't really want to know the details there). In this case, >there are n 9's total. >Of course, I've pointed this out before to you, and so far it's >yet to sink in, unlike the iron spike in the case of Phinehas Gage. >(ObOuch: Ouch.) >Unfortunately, to most calculators, all numbers are rationals -- >furthermore, to modern computers, all numbers are multiples of a >power of 2, with some fudging on the arithmetic side to make it >look otherwise. (The standard representation is r = 2^e * M, where >M is up to about 53 bits and e can range from -2048 to +2047 >or thereabouts.) Therefore, a partial sum may yield anomalies >if not done carefully. >For example, to a computer, >1/3 = 0x3fd5555555555555 . >This is readily verified using C and a hack such as the following: >#include >int main() > union { unsigned char c[sizeof(double)]; double d; } u; > int i; > u.d = 1.0/3.0; > printf(1/3 = 0x); > for(i=0;i printf(n); > return 0; >(Depending on machine the hex values will print either >forwards or backwards. If it's a worry, use something like >#include >and >#if BYTE_ORDER == BIG_ENDIAN >in appropriate spots.) >The first bit is the sign bit; the next 11 is a modified exponent, >and the rest are the mantissa, with a hidden-1. For example, >1.0 = 0x3ff0000000000000 >2.0 = 0x4000000000000000 >3.0 = 0x4008000000000000 >4.0 = 0x4010000000000000 >5.0 = 0x4014000000000000 >In a very real sense, to a computer >1/3 = 6004799503160661/18014398509481984 >= .333333333333333314829616256247390992939472198486328125 . >(Note that 15555555555555(16) = 6004799503160661(10).) >One can use an infinite-precision calculator such as bc to >derive these results: >$ bc <ibase=16 >15555555555555 >6004799503160661 >Now multiply by 3, and one gets >18014398509481983/18014398509481984 >= .999999999999999944488848768742172978818416595458984375 . >Is 1 = .999999999999999944488848768742172978818416595458984375 ? >Certainly not. But computers aren't as bright as one might think. :-) >I'll also mention a little bug in Microsoft's calculator. Microsoft >(or an engineer therein) was apparently somewhat naive, and one got >3.11 - 3.10 = 0.00 >in their calculator in Win95. >It turns out that >3.11 = 0x4008e147ae147ae1 >3.10 = 0x4008cccccccccccd >diff = 0x3f847ae147ae1400 >0.01 = 0x3f847ae147ae147b >so, to a computer, (3.11 - 3.10) is just a smidge less than 0.01. >With rounding this ordinarily isn't a problem, but if one forgets >to round -- well, one very well might get 0.00, with an invisible >9 for one's trouble. >The bug finally got fixed some time ago, but it took awhile. >Another illustration is 9007199254740992+1 = 9007199254740992, >if one uses double. Not a lot one can do about it without >switching away from double (e.g., one might use long long >instead), as the bit gets lost; 2^53 = 9007199254740992. >It gets worse. >Remember that the exact representation of 1/3 using double >precision is >1/3 = .333333333333333314829616256247390992939472198486328125 >A naive C program using %.60f (which is waaay too much precision >and not enough accuracy!) gives >1/3 = .333333333333333314829616256247390992939472198486328125 >which actually turns out to be the right answer -- if one can >call this a right answer. >However, a naive progressive digitation algorithm prints out >1/3 = .333333333333333303727386009995825588703155517578125 >Yipes. >The conclusion: don't depend on partial sums generated by computer, >unless you know exactly what it's doing -- and what you're doing. >[.sigsnip] >-- >#191, ewill3@earthlink.net >It's still legal to go .sigl LEARN MATH. http://mathworld.wolfram.com/HyperrealNumber.html .999... < 1 .999... =/= 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >I won this debate years ago. So what is the reason to start it again? === Subject: Re: .99999... still=/= 1 >>I won this debate years ago. >So what is the reason to start it again? To make me feel better by about this much, 99.999...% . Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 Let's look at another approach to this. You say, 1 = .999... well let's see, function1 f(n)_1 = 1 function2 f(n)_2 = 9/10^n Does, f(n)_1 = f(n)_2 ? If we integrate (from 0 to oo) it should show that each function is equal, if 1 = .999... . Integrate the function f(n)_2 = 9/10^n from 0 to oo and compare this with the Integration of the function f(n)_1 = 1 from 0 to oo, both with respect to n. Integral ( 0 to oo) 1 dn = n ( 0 to oo) = oo - 0 = oo Integral ( 0 to oo ) 9/10^n dn 9/10^n ( 0 to oo) = 9/10^oo - 9/10^0 = 0 - 9 = -9 ( assume 9/10^oo -->0) If 1 = .999.., then the integration value from 0 to oo for both functions should be the same and they are not. -9 =/= oo .999... =/= 1 f(n)_1 =/= f(n)_2 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 Let's look at another approach to this... If .999... = 1 then, 2.999... X 10^8m/sec This should occur. 2.999... X 10^8m/sec ---> 3.0 X 10^8m/sec reach the speed of light and cause .999... = 1, which would make, 2.999... X 10^8m/sec --> 3 X 10^8 m/sec ------------------------------------------------------- Another approach to this in energy aspects of .999... and 1 is : Write a computer program. 10 n = 1 20 print n run program 1 Very little energy needed to run this program. Now try this. 5 a = 0 10 For n = 1 to oo 20 a = a + 9/10^n 30 If a = 1 then 50 40 next n 50 print a run It will take an infinite amount of energy to run this program. It will never reach 1. Just like accelerating matter near the speed of light, you need an infinite amount of energy to reach the speed of light, according to Einstein. So with respect to matter and energy, .999... =/= 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > reach the speed of light and cause .999... = 1, which would make, This has nothing to do with dividing by zero. Besides there is only a finite amount of energy in the entire physical cosmos. So the upperbound Bob Kolker === Subject: Re: .99999... still=/= 1 >could >> reach the speed of light and cause .999... = 1, which would make, >This has nothing to do with dividing by zero. Besides there is only a >finite amount of energy in the entire physical cosmos. So the upperbound >Bob Kolker Mathematics can lead a person to fairy tale land. It's important to try your best to see what science shows with experimental evidence, THEN math can be applied to it. We can see in physical reality that .999... can't = 1 because it can't reach it. This is proven in reality. I noticed you snipped the part about the computer program never reaching 1 from .999... , but anyway we can see in reality, 1) the tooth fairy doesn't exist 2) the fairy godmother doesn't exist and 3) .999... = 1 Math trickery and math illusions was used in the development of the Periodic Table of Elements, too. They made believe that electron orbitals existed and then made a math story of how it could actually work. But reality is beginning to show us with real atomic images that electrons don't show orbitals but intelligence logic structures. The Smart Model predicted this about 10 years before they knew it. I have shown you repeatedly ..., that everything even in math, and in physical reality shows ust that, .999... =/= 1 If you want to believe .999... = 1, it's up to you, but it doesn't. You may ask how can light reach 3.0 X 10^8 m/sec when matter can't. This is because photons start at a unified state or oneness, of this amount of energy. It doens't start with .999... and then reaches 1. It is 1, that is 1 with itself at that energy state, to start with. Can someone else be you? No, because you are 1. You are you. Others may try to reach you .999... ---> 1 you, but you will always be unique, and only you. An exact clone of you can never be made, because .999... can't reach 1. You can make close clones of something ( .999...), but not the exact clone, 1. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 decimally, the speed of light is 1.0000... lightyears/year. > Mathematics can lead a person to fairy tale land. It's important to try your --4my of it? http://www.wlym.com === Subject: Re: .99999... still=/= 1 I mean, *exactly* 1.0000... lightmoments per moment, but only in vacuo, which never actually occurs. --4my of it? http://www.wlym.com === Subject: Re: .99999... still=/= 1 > You may ask how can light reach > 3.0 X 10^8 m/sec when matter can't do photons move at light speed (in vacuo), they cannot move at any other speed. energy will take it to light speed. There is only a finite amount of energy in the kosmos so it is impossible for any massive body to move at light speed. Bob Kolker === Subject: Re: .99999... still=/= 1 >> You may ask how can light reach >> 3.0 X 10^8 m/sec when matter can't >do photons move at light speed (in vacuo), they cannot move at any other >speed. So, .999... can't apply to photons. But can apply to mass. >energy will take it to light speed. There is only a finite amount of >energy in the kosmos so it is impossible for any massive body to move at >light speed. >Bob Kolker Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > At one digit less than oo, ( assuming you really reach infinity) the nth > term reaches 0 so, .999... reaches 0 not 1. And what is the decimal digit of pi at the infinity? > Even if you go past oo by one digit, it still doesn't reach 1. In which direction the wind blows at that point? === Subject: Re: .99999... still=/= 1 >> At one digit less than oo, ( assuming you really reach infinity) >the nth >> term reaches 0 so, .999... reaches 0 not 1. >And what is the decimal digit of pi at the infinity? I already answered that. First of all pi ISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS an irrational number, the decimal values vary. It can not be determined. But with a repeating decimal, you can use a non-standard approach and use one digit less than oo then, n-->oo -1 lim 9/10^n ---> 90/10^oo ^ | last digit seen is zero right before infinity. It never reaches 1. >> Even if you go past oo by one digit, it still doesn't reach 1. >In which direction the wind blows at that point? Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >> At one digit less than oo, ( assuming you really reach infinity) >the nth >> term reaches 0 so, .999... reaches 0 not 1. >And what is the decimal digit of pi at the infinity? > I already answered that. First of all pi > ISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS an > irrational number, the decimal values vary. It can not be determined. But with > a repeating decimal, you can use a non-standard approach and use one digit less > than oo then, > n-->oo -1 > lim 9/10^n ---> 90/10^oo > ^ > | > last digit seen is zero right before infinity. It never reaches 1. There is no right before infinity. === Subject: Re: .99999... still=/= 1 >>> At one digit less than oo, ( assuming you really reach infinity) >>the nth >>> term reaches 0 so, .999... reaches 0 not 1. >> >>And what is the decimal digit of pi at the infinity? >> I already answered that. First of all pi >> ISSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS an >> irrational number, the decimal values vary. It can not be determined. But >with >> a repeating decimal, you can use a non-standard approach and use one digit >less >> than oo then, >> n-->oo -1 >> lim 9/10^n ---> 90/10^oo >> ^ >> | >> last digit seen is zero right before infinity. It never reaches 1. >There is no right before infinity. I said the digit right before oo. REFERENCE MATHCAD PROFESSIONAL Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > | > last digit seen is zero right before infinity. It never reaches 1. There is no right before infinity, numbskull. Your comprehension of mathematics is infitesimally small. A hyperreal equivalent of 0. Bob Kolker === Subject: Re: .99999... still=/= 1 >> | >> last digit seen is zero right before infinity. It never reaches 1. >There is no right before infinity, numbskull. Hey, there are probably about 1 million supporters using MathCAD Professional. This is an industry standard for math for scientists and engineers. A non-standard approach using MathCAD clearly shows that, n-->oo -1 lim 9/10^n ---> 90/10^n The digit right before oo for the hyperreal number or series .999... is 0. Therefore, there is a space existing between, .999... and 1 so, as the definition of a hyper-real number implies, .999... < 1 A hyper-real number causes a space to exist between it and a real number. 1 is the real number .999... is the hyper-real number that forms the space between the two. So, .999... =/= 1 .999... < 1 >Your comprehension of mathematics is infitesimally small. A hyperreal >equivalent of 0. >Bob Kolker Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 In sci.math, S. Enterprize Company > | > > last digit seen is zero right before infinity. It never reaches 1. >>There is no right before infinity, numbskull. > Hey, there are probably about 1 million supporters using MathCAD > Professional. This is an industry standard for math for scientists and > engineers. A non-standard approach using MathCAD clearly shows that, > n-->oo -1 > lim 9/10^n ---> 90/10^n > The digit right before oo for the hyperreal number or > series .999... is 0. Therefore, there is a space existing between, > .999... and 1 so, > as the definition of a hyper-real number implies, > .999... < 1 An interesting notion, that. So D[.999..., w-1] = 0, eh? [*] What is D[.999..., w-2]? How about D[.999..., w/2]? It's easily proven that, if D[.999..., n] = 9, then D[.999...., n+1] = 9 as well (the simplest method arguably is to evaluate D[x*10, n]), for any finite n. Not sure if w-1 is finite or not -- or even meaningful. As for MathCAD: that's a program, an approximation of reality. Not that real numbers are all that real, anyway -- they're mathematical/symbolic abstractions, there because Dedekind, Cauchy, and Cantor and others needed more numbers for set theory. In light of what I've written before regarding 1/3, one might have to verify the results carefully. > A hyper-real number causes a space to exist between it and a real number. > 1 is the real number > .999... is the hyper-real number that forms the space between the two. > So, > .999... =/= 1 > .999... < 1 Your logic is extremely sloppy, though your conclusion is interesting. I'm just not sure which realm it exists in, although the standard real realm does not contain it (the standard realm doesn't contain any numbers between 0 and all 1/n, n > 0, n in J: the hyperreal realm, however, does). [.sigsnip] [*] I don't have an omega, so I'm using 'w' here to indicate the first transfinite ordinal. Is there a w_0, analogous to the cardinal aleph_0? This gets a bit messy. D[r,n] = the digit associated with the n'th decimal place after the decimal point (e.g., D[.98765, 4] = 6). -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 >In sci.math, S. Enterprize Company > >> | >> >> last digit seen is zero right before infinity. It never reaches 1. >There is no right before infinity, numbskull. >> Hey, there are probably about 1 million supporters using MathCAD >> Professional. This is an industry standard for math for scientists and >> engineers. A non-standard approach using MathCAD clearly shows that, >> n-->oo -1 >> lim 9/10^n ---> 90/10^n >> The digit right before oo for the hyperreal number or >> series .999... is 0. Therefore, there is a space existing between, >> .999... and 1 so, >> as the definition of a hyper-real number implies, >> .999... < 1 >An interesting notion, that. So D[.999..., w-1] = 0, eh? [*] >What is D[.999..., w-2]? How about D[.999..., w/2]? Using MathCAD I get, n-->oo - 2 lim 9/10^n ---> 900/10^oo How can this be interpreted? In a non-standard analysis, in my opinion, it could be mean we are moving further away from 1, but we still maintain the surreal number or hyperreal number. For n digits less than infinity .999..n | 1 you still get, .999... < 1 For the case 1/2 a digit less than infinity, MathCAD calls this a bidirectional limit. n-->oo/2 lim 9/10^n --> 9/((10^oo)^1/2) But I don't think this applies to a surreal or a hyperreal number. .999... doesn't really exist anymore. So I don't think you can say this. >It's easily proven that, if D[.999..., n] = 9, then D[.999...., n+1] = 9 Ok, because, If the mth digit less than oo = oo n--> oo - m lim 9/10^oo-oo ---> 9 What can this be interpreted as in regard to a surreal number? It looks like to me, in this case we have totally removed the original hyperreal or surreal number. I think there is a limit to how far you can go minus digits before you change, .999... totally from it original form. In this case, you no longer have, .999..., you have something else. You have just 9. This isn't surreal or hyperreal. >as well (the simplest method arguably is to evaluate D[x*10, n]), >for any finite n. Not sure if w-1 is finite or not -- or even meaningful. >As for MathCAD: that's a program, an approximation of reality. Not that >real numbers are all that real, anyway -- they're mathematical/symbolic >abstractions, there because Dedekind, Cauchy, and Cantor and others needed >more numbers for set theory. In light of what I've written before >regarding 1/3, one might have to verify the results carefully. >> A hyper-real number causes a space to exist between it and a real number. >> 1 is the real number >> .999... is the hyper-real number that forms the space between the two. >> So, >> .999... =/= 1 >> .999... < 1 >Your logic is extremely sloppy, though your conclusion is interesting. Why would it be sloppy to you? Do you mean as far as accuracy is concerned? >I'm just not sure which realm it exists in, although the standard >real realm does not contain it (the standard realm doesn't >contain any numbers between 0 and all 1/n, n > 0, n in J: the hyperreal >realm, however, does). >[.sigsnip] >[*] I don't have an omega, so I'm using 'w' here to indicate the > first transfinite ordinal. Is there a w_0, analogous to > the cardinal aleph_0? This gets a bit messy. > D[r,n] = the digit associated with the n'th decimal place > after the decimal point (e.g., D[.98765, 4] = 6). >-- >#191, ewill3@earthlink.net >It's still legal to go .sigless. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >> Yes the limit is exactly 1 in reals. > And also in the hyperreals. >> Yes, if you count the limit over reals plus over hyperreals. Sorry - I >> cannot find better word than over. Find a better word as your mother >> language is English. >> I try to specify: >> As you count the limit in reals, then N --> oo, where every N is finite >> integer. As you count the limit over hyperreals, then N_inf -->oo_inf, >> where >> oo_inf has higher cardinality as the cardinality of N_inf >N. > No, this is not about cardinality at all. The infinitely large integers > of NSA are not the same as transfinite cardinals. It's necessary to observe: As the cardinality of reals R > cardinality of integers N, so the cardinality of N_inf > N. As you count the limit N --->oo instead of N-inf, then you certainly omit something - namely hyperreal part. >> N (finite integers) does not cover hyperreal area, i.e. the numbers >> smaller >> than reals, because N hardly covers real area as discussed under the >> thread >> Are reals well-ordered. >> As we count the real limit in NSA, then the hyperreals exist, but they >> are >> not counted in limit as N -->oo, but not as N_inf -->oo. Hyperreals are >> omitted and therefore 0.999...<1 in hyperreals, though the real part of >> the >> limit equals to 1. > I take it you mean the standard part of the limit is 1. Well, we can talk about standard part and non-standard part, if you prefer this. > That happens to > be true, but for a trivial reason. The limit itself is exactly 1, and > the standard part of 1 is simply 1. Cases: 1)Yes, the limit is exactly 1only if you count the limit including the non standard part as N-inf --->oo. Then your reference set is N_inf. 2)Yes, the limit is exactly 1only if you count the limit including the standard part as N --->oo. Then your reference set is N. 3) But..., if you count the limit including the standard part as N --->oo and your reference set is N_inf, then you omit non-standard part. As a consequence in this last case 0.999...<1 in N_inf. >> NSA expands the concept of numbers to >> the numbers that are smaller than any real, i.e epsilon environment. >> This >> is >> equivalent with the concept of epsilon delta theorem. Read literally >> what >> epsilon delta theorem says. This was learnt us already in 70Ēs in >> university. Are you back in 50's? > Which part of my statement do you not accept? Do you disagree with the > definition I gave? >> Explained above. > Try again. You didn't mention any part of the definition, let alone say > which part you disagreed with. > Definition. Let { a_k } be a sequence and let L be a real number. > We say lim_{k->oo} a_k = L if, for every epsilon > 0, there exists > N > 0 such that | a_k - L | < epsilon for every k > N. > Remark 1. Exactly the same definition applies to standard analysis and > to nonstandard analysis, with the proviso that in NSA the epsilon > 0 > is allowed to be an infinitesimal and the N > 0 is allowed to be > infinitely large. Yes, agreed. > Remark 2. The definition does not say what it means for the limit to be > close to L. The definition only says what it means for the limit to be > equal to L. Either the definition is satisfied, or it isn't. OK. > Now, the questions: (1) Do you agree with the definition? (2) Do you > agree that according to this definition the limit is exactly 1, even in > NSA? If you don't agree, explain why not. Yes, I do agree as explained above in the cases 1 and 2. You did not consider at all the case 3 above. How does your definitions should be applied on the case 3? You should also note that the limit is the upper boundary value. As you will see below, it's not the question about the limit but about AC and the point of reference as we construct the numbers integers, infinite integers, reals, hyperreals etc. > For example, try to give a > particular value of epsilon > 0 such that the definition is not > satisfied. Hint: choosing an infinitesimal epsilon is allowed, but it > won't help your case. The definition still works. What about case 3 above as you stop epsilons in standard part omitting non-standard part. >> I would like to ask the same from You. :-). Is it the point >> of reference that is strange concept for You? > Point of reference is an undefined concept and does not appear in the > definition of limit, quoted above. I won't comment on whether it is > strange, since things have to be defined first before they can possibly > qualify as strange. The point of reference is counting point reference, which also separates infinities. The standard point of reference is the normal decimal dot that separates the integer part and the decimal part, which can be infinite long string. Without the point of reference you do not know which part is integer part and which one is the decimal part. What ever you calculate you always refer your calculations to some point of reference. >> In fact, there seems to be a slight conceptual difference in our >> argumentation. The difference is analocigally the same as we talk about >> finite decimal numbers. You accept that finite 0.99999 <1, as there are >> no >> infinite 9's. As hyperreals are omitted in the real limit counting (not >> counted over hyperreals), then in reals the limit equals to 1, i.e. >> 0.999...=1. But as hypereals exist, but omitted in the limit calculation, >> then 0,999...<1 in NSA. Simple as possible. Reals are finite from the >> hypereal point of view. Therefore 0.999...<1 - in hyperreals as only real >> area is considered. > But in NSA there is no such thing as a .999... that extends only through > finite digit positions. If the string is infinitely long, then it > necessarily extends to infinite digit positions in NSA. That may sound > vaguely similar to an argument commonly made by cranks, but the > difference is that the cranks are not talking about NSA. used the case 3 as an example to point out how the people do not think as their argumentation contains hidden asumptions. So - if there exist non-standard part, which is purposely omitted, then you do not calculate the total or over-all limit. In this case you have to observe that there are numbers smaller than any real number and as a consequence 0.999... cannot be equal to 1, though the limit equals to 1. What is this paradox, which has been the reason to this thread, and how do we fix it? The solution is to point out that the limit is a mathematical upper boundary value, but does not tell the real value of the string but the next, i.e. successor, value of the string, because the limit calculation is based on the epsilon delta theorem. > The definition of a limit in NSA may be stated in various ways, but all > of them are equivalent to the usual epsilon-delta definition, with the > proviso that epsilons and deltas are allowed to be infinitesimal, and N > is allowed to be infinitely large. >> Yes, that's what I mean - too, assuming we mean the same thing. If you >> limit >> your calculation into the real area and omit the hyperreal area, > You can't do that. That's the whole point. LetĒs demontrate it shortly now so simply as possible (like Donald Knuth 1) It is assumed that the digits [0,1...9] in 10-base system are constructed. I leave it for the home work. 2) Then we apply AC so that we have infinite many placeholders (or hooks) with the first one and the last one (the start and the end), just like in [0,1]. (by the way this stops the discussion about the last digit in the infinite decimal string. :-)) For us it's enough that is just possible. 3) Pick-up with the aid of AC some digits in every placeholder. What number do you have? Actually you have just digits, but not a number - yet. Why? Because you have not defined the point of reference! You have only digits in every place holder, i.e. in every hook. 4) Adjust the digits, you have picked up by hooks, into a linear string. It's infinite, but it has the start and the end. Additionally we define (in this particular 10 base case) what is the relation of the adjacent placeholders. What number do you have now? No number, because you just have the linear infinite string without the point of reference. The point of reference defines the infinite string area, but we do not have it yet, thus as a consequence - no number area. 5) Apply the the point of reference. How? You can insert the point of reference anywhere in the string, but let's concentrate our attention into two special case because of simplicity: to the left hand side (lhs) of the infinite string or to the right hand side (rhs). What kind of point of reference? Any defined kind, but let's apply because of the simplicity the standard point of reference that is called the decimal dot (or mark). Let's insert the standard point of reference into lhs of the string. What number do you have? It is familiar decimal number depending on the values of digits in the string. Is it rational, irrational or transcendental depending on the digits. If there are only zeros on rhs starting from some placeholders, then the decimal part is called finite. Let's insert the standard point of reference into rhs of the string. What number do you have? It looks like now an integer, but isn't it integer?. It's infinite long with start and end. It's somehow finite, but anyway infinite. Integers cannot be infinite? Yes, they can. Actually every classic finite integer (N) can be written as infinite, if there are only zeros on lhs starting from some placeholders. In other case we call them infinite integers (N_inf). As an observation we recognize immediately that there is one-to-one bijection between N_inf and decimal part of R. The only difference is that N_inf has the standard point of reference on rhs and R (decimal part) has the standard point of reference on lhs. The standard point of reference, i.e. the decimal dot separates to two infinite long strings. Both parts are constructed by AC. The only difference is the point of reference on lhs or on rhs. As finite integers (N) are the subset of infinite integers (N_inf). AC, Zorn's lemma and well-ordering are equivalent. Integers and infinite integers are well-ordered. By moving the point of reference from rhs (in N_inf) to lhs (in R, decimal part) it's trivial to recognize that the decimal part is also well-ordered. Considering the limit, it's easy to observe that if the point of reference is on lhs of the string of infinite 9's, i.e. 0.999..., the limit equals to 1. But if the point of the reference is on rhs of the same string, then there is no limit, because we cannot calculate it for N_inf like ...999. We can add 1 to ...999, but then - as all the placeholders were occupied with 9's in the infinite long string - the successor equals to omega 1. Thus the limit, i.e. the upper boundary value, describes the successor, not the sum of the string itself as it should count. Successor equals never with the precessor and therefore omega 1> ...999 and also 1>0.999... The reason is AC and well-ordering. Thus for example a general number can be described omega-area (separator) infinite integer area (separator, usually dot), decimal area (separator) non-standard area. Each area is infinite and well-ordered constructed with the aid of AC. We don't have to use the standard approach one first defines Z, then defines Q, then defines R, each in different ways. Dedekind cut is not necessary but useful, which is another thing. All we need is AC and the point of reference. Tapio > -- > Dave Seaman > Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. > === Subject: Re: .99999... still=/= 1 > Yes, if you count the limit over reals plus over hyperreals. Sorry - I > cannot find better word than over. Find a better word as your mother > language is English. > I try to specify: > As you count the limit in reals, then N --> oo, where every N is finite > integer. As you count the limit over hyperreals, then N_inf -->oo_inf, > where > oo_inf has higher cardinality as the cardinality of N_inf >N. >> No, this is not about cardinality at all. The infinitely large integers >> of NSA are not the same as transfinite cardinals. > It's necessary to observe: As the cardinality of reals R > cardinality of > integers N, so the cardinality of N_inf > N. As you count the limit > N --->oo instead of N-inf, then you certainly omit something - namely > hyperreal part. All very confused. Assuming you mean N_inf = *N, the set of hyperintegers, then it's true that *N as an external set has the cardinality of the reals, but the internal set *N has a *cardinality equal to *aleph_0. This certainly doesn't mean that the hypernaturals are the same as transfinite cardinals. For one thing, there is a smallest transfinite cardinal (aleph_0), but there is no such thing as a smallest infinite hypernatural. If n is an infinitely large integer, then so is n-1. And none of this has anything to do with limits. You seem to think that infinity has only one meaning in all of mathematics. Wrong. > N (finite integers) does not cover hyperreal area, i.e. the numbers > smaller > than reals, because N hardly covers real area as discussed under the > thread > Are reals well-ordered. > As we count the real limit in NSA, then the hyperreals exist, but they > are > not counted in limit as N -->oo, but not as N_inf -->oo. Hyperreals are > omitted and therefore 0.999...<1 in hyperreals, though the real part of > the > limit equals to 1. >> I take it you mean the standard part of the limit is 1. > Well, we can talk about standard part and non-standard part, if you prefer > this. I'm trying to guess what you might mean by the real part, since you have not defined your meaning. We are not talking about complex numbers here. >> That happens to >> be true, but for a trivial reason. The limit itself is exactly 1, and >> the standard part of 1 is simply 1. > Cases: > 1)Yes, the limit is exactly 1only if you count the limit including the non > standard part as N-inf --->oo. Then your reference set is N_inf. I don't know what you mean by the reference set is N_inf. The sum is over *N. > 2)Yes, the limit is exactly 1only if you count the limit including the > standard part as N --->oo. Then your reference set is N. Are you talking about standard analysis here, or nonstandard? The set N (consisting of the finite naturals) is not a set in the internal set theory of NSA. Its counterpart is *N, which includes the infinitely large naturals. If you are forming a sum in NSA, then you can sum over *N, but not over N. > 3) But..., if you count the limit including the standard part as N --->oo > and your reference set is N_inf, then you omit non-standard part. As a > consequence in this last case 0.999...<1 in N_inf. That's all very confused, but I think you are trying to say that the limit of the sequence { 1 - 1/10^n } in NSA has a nonzero nonstandard part. False. The limit is exactly 1 according to the definition I gave previously. Perhaps what is confusing you is the following fact from NSA: Theorem. Let { a_k } be a sequence and L a real number. Then the following statements are equivalent: (1) lim_{k->oo} a_k = L. (2) The difference | a_k - L | is an infinitesimal whenever k is infinitely large. Notice, however, that neither (1) nor (2) says anything about the limit differing from L by an infinitesimal. Statement (1) mentions the limit, but it's a statement of exact equality. Statement (2) mentions something that differs from L by an infinitesimal, but it makes no mention of the limit whatsoever. Either way you look at it, neither of these statements supports your conclusion for the case a_k = 1 - 1/10^k and L = 1. > NSA expands the concept of numbers to > the numbers that are smaller than any real, i.e epsilon environment. > This > is > equivalent with the concept of epsilon delta theorem. Read literally > what > epsilon delta theorem says. This was learnt us already in 70Ēs in > university. Are you back in 50's? >> Which part of my statement do you not accept? Do you disagree with the >> definition I gave? > Explained above. >> Try again. You didn't mention any part of the definition, let alone say >> which part you disagreed with. >> Definition. Let { a_k } be a sequence and let L be a real number. >> We say lim_{k->oo} a_k = L if, for every epsilon > 0, there exists >> N > 0 such that | a_k - L | < epsilon for every k > N. >> Remark 1. Exactly the same definition applies to standard analysis and >> to nonstandard analysis, with the proviso that in NSA the epsilon > 0 >> is allowed to be an infinitesimal and the N > 0 is allowed to be >> infinitely large. > Yes, agreed. >> Remark 2. The definition does not say what it means for the limit to be >> close to L. The definition only says what it means for the limit to be >> equal to L. Either the definition is satisfied, or it isn't. > OK. >> Now, the questions: (1) Do you agree with the definition? (2) Do you >> agree that according to this definition the limit is exactly 1, even in >> NSA? If you don't agree, explain why not. > Yes, I do agree as explained above in the cases 1 and 2. You did not > consider at all the case 3 above. How does your definitions should be > applied on the case 3? There is no case 3 above. I don't know what you are talking about. > You should also note that the limit is the upper boundary value. As you will > see below, it's not the question about the limit but about AC and the point > of reference as we construct the numbers integers, infinite integers, reals, > hyperreals etc. >> For example, try to give a >> particular value of epsilon > 0 such that the definition is not >> satisfied. Hint: choosing an infinitesimal epsilon is allowed, but it >> won't help your case. The definition still works. > What about case 3 above as you stop epsilons in standard part omitting > non-standard part. There is no case 3 above. I have explained that the sum over N is not a sum in NSA, since N is not an internal set in NSA. That's why we sum over *N instead. > I would like to ask the same from You. :-). Is it the point > of reference that is strange concept for You? >> Point of reference is an undefined concept and does not appear in the >> definition of limit, quoted above. I won't comment on whether it is >> strange, since things have to be defined first before they can possibly >> qualify as strange. > The point of reference is counting point reference, which also separates > infinities. That is not a definition. For an example of what I mean by a definition, look at my definition of what it means to say that lim_{k->oo} a_k = L. Mathematical definitions leave no room for fuzzy language or vague concepts. Try again. > The standard point of reference is the normal decimal dot that separates the > integer part and the decimal part, which can be infinite long string. > Without the point of reference you do not know which part is integer part > and which one is the decimal part. What ever you calculate you always refer > your calculations to some point of reference. The common definitions of the real numbers (via Dedekind cuts or Cauchy sequences) do not mention decimal points at all and do not depend on any such concepts as integer part and decimal part. For any real number x, the integer part of x may be defined as floor(x) = max { n in N : n <= x }. I had no need for any vague concepts such as point of reference in writing that definition. > In fact, there seems to be a slight conceptual difference in our > argumentation. The difference is analocigally the same as we talk about > finite decimal numbers. You accept that finite 0.99999 <1, as there are > no > infinite 9's. As hyperreals are omitted in the real limit counting (not > counted over hyperreals), then in reals the limit equals to 1, i.e. > 0.999...=1. But as hypereals exist, but omitted in the limit calculation, > then 0,999...<1 in NSA. Simple as possible. Reals are finite from the > hypereal point of view. Therefore 0.999...<1 - in hyperreals as only real > area is considered. You need to be precise about what you mean by 0.999... in NSA. I have been taking it to mean the sum of 9/10^n for all n in *N, n > 0. You evidently mean something different. In particular, it can't possibly mean the sum over all finite values of n > 0, because that is not a set in NSA. >> But in NSA there is no such thing as a .999... that extends only through >> finite digit positions. If the string is infinitely long, then it >> necessarily extends to infinite digit positions in NSA. That may sound >> vaguely similar to an argument commonly made by cranks, but the >> difference is that the cranks are not talking about NSA. > used the case 3 as an example to point out how the people do not think as > their argumentation contains hidden asumptions. So - if there exist > non-standard part, which is purposely omitted, then you do not calculate the > total or over-all limit. In this case you have to observe that there are > numbers smaller than any real number and as a consequence 0.999... cannot be > equal to 1, though the limit equals to 1. > What is this paradox, which has been the reason to this thread, and how do > we fix it? If you do not sum 9/10^n for all n > 0, then you are not computing 0.999.... The indicated sum is exactly 1. > The solution is to point out that the limit is a mathematical upper boundary > value, but does not tell the real value of the string but the next, i.e. > successor, value of the string, because the limit calculation is based on > the epsilon delta theorem. The string I am talking about has no successor values. It's already defined for all positions n, including the ones that are infinitely large. >> The definition of a limit in NSA may be stated in various ways, but all >> of them are equivalent to the usual epsilon-delta definition, with the >> proviso that epsilons and deltas are allowed to be infinitesimal, and N >> is allowed to be infinitely large. > Yes, that's what I mean - too, assuming we mean the same thing. If you > limit > your calculation into the real area and omit the hyperreal area, >> You can't do that. That's the whole point. > LetĒs demontrate it shortly now so simply as possible (like Donald Knuth > 1) It is assumed that the digits [0,1...9] in 10-base system are > constructed. I leave it for the home work. > 2) Then we apply AC so that we have infinite many placeholders (or hooks) > with the first one and the last one (the start and the end), just like in > [0,1]. We don't need AC here. We are defining d_0 = 0 and d_k = 9 for all k > 0 in *N. > (by the way this stops the discussion about the last digit in the infinite > decimal string. :-)) For us it's enough that is just possible. I was not aware that there was any such discussion. > 3) Pick-up with the aid of AC some digits in every placeholder. Again, AC is irrelevant. We already have our hyperinfinite string. > What number do you have? Actually you have just digits, but not a number - > yet. Why? Because decimal digit strings are not numbers. They merely represent numbers. > Because you have not defined the point of reference! You have only digits in > every place holder, i.e. in every hook. Nonsense. If { d_k } is a decimal digit string, then the number represented by the string is sum_{k in *N} d_k * 10^(-k). No point of reference is needed. [ snip nonsense about point of reference ] -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 >> Yes, if you count the limit over reals plus over hyperreals. Sorry - I >> cannot find better word than over. Find a better word as your mother >> language is English. >> I try to specify: >> As you count the limit in reals, then N --> oo, where every N is finite >> integer. As you count the limit over hyperreals, then N_inf -->oo_inf, >> where >> oo_inf has higher cardinality as the cardinality of N_inf >N. > No, this is not about cardinality at all. The infinitely large integers > of NSA are not the same as transfinite cardinals. We talk about ordinals. That above was just a hint to compare the cardinality of N_inf and N. >> It's necessary to observe: As the cardinality of reals R > cardinality of >> integers N, so the cardinality of N_inf > N. As you count the limit >> N --->oo instead of N-inf, then you certainly omit something - namely >> hyperreal part. > All very confused. Assuming you mean N_inf = *N, the set of > hyperintegers, then it's true that *N as an external set has the > cardinality of the reals, but the internal set *N has a *cardinality > equal to *aleph_0. This is of-course OK! > This certainly doesn't mean that the hypernaturals > are the same as transfinite cardinals. For one thing, there is a > smallest transfinite cardinal (aleph_0), Ok! > but there is no such thing as a > smallest infinite hypernatural. If n is an infinitely large integer, > then so is n-1. Omega was defined in this discussion earlier as follows: The number that is greater than any infinite integer. That is the smallest transinfinite number. Omega is the successor of ...999, i.e. n+1. The precessor (n-1) of ...999 is ...998. > And none of this has anything to do with limits. You seem to think that > infinity has only one meaning in all of mathematics. Wrong. Your opinion. :-) >> N (finite integers) does not cover hyperreal area, i.e. the numbers >> smaller >> than reals, because N hardly covers real area as discussed under the >> thread >> Are reals well-ordered. >> As we count the real limit in NSA, then the hyperreals exist, but they >> are >> not counted in limit as N -->oo, but not as N_inf -->oo. Hyperreals are >> omitted and therefore 0.999...<1 in hyperreals, though the real part of >> the >> limit equals to 1. > I take it you mean the standard part of the limit is 1. >> Well, we can talk about standard part and non-standard part, if you >> prefer >> this. > I'm trying to guess what you might mean by the real part, since you > have not defined your meaning. the real part was the decimal part - as you certainly knew. > We are not talking about complex numbers > here. Exactly! > That happens to > be true, but for a trivial reason. The limit itself is exactly 1, and > the standard part of 1 is simply 1. >> Cases: >> 1)Yes, the limit is exactly 1only if you count the limit including the >> non >> standard part as N-inf --->oo. Then your reference set is N_inf. > I don't know what you mean by the reference set is N_inf. The sum is > over *N. That is exactly what I meant above if N_inf=*N. >> 2)Yes, the limit is exactly 1only if you count the limit including the >> standard part as N --->oo. Then your reference set is N. > Are you talking about standard analysis here, or nonstandard? Standard analysis as You correctly observed. > The set N > (consisting of the finite naturals) is not a set in the internal set > theory of NSA. Coorect, but it should be as *N is the extension of the set N. > Its counterpart is *N, which includes the infinitely > large naturals. If you are forming a sum in NSA, then you can sum over > *N, but not over N. We can sum over subset too. >> 3) But..., if you count the limit including the standard part as >> N --->oo >> and your reference set is N_inf, then you omit non-standard part. As a >> consequence in this last case 0.999...<1 in N_inf. > That's all very confused, but I think you are trying to say that the > limit of the sequence { 1 - 1/10^n } in NSA has a nonzero nonstandard > part. False. The limit is exactly 1 according to the definition I gave > previously. N is the subset of *N. You can count the limit over N or alternatively over *N as You can count N --> 0 to 1000 as a subset of N or alternatively N --->0 to oo. > Perhaps what is confusing you is the following fact from NSA: > Theorem. Let { a_k } be a sequence and L a real number. Then the > following statements are equivalent: > (1) lim_{k->oo} a_k = L. > (2) The difference | a_k - L | is an infinitesimal > whenever k is infinitely large. > Notice, however, that neither (1) nor (2) says anything about the limit > differing from L by an infinitesimal. Yes, as long as you count over *N > Statement (1) mentions the limit, > but it's a statement of exact equality. Statement (2) mentions something > that differs from L by an infinitesimal, but it makes no mention of the > limit whatsoever. Except Yount count over N instead of *N. > Either way you look at it, neither of these statements > supports your conclusion for the case a_k = 1 - 1/10^k and L = 1. >> NSA expands the concept of numbers to >> the numbers that are smaller than any real, i.e epsilon environment. >> This >> is >> equivalent with the concept of epsilon delta theorem. Read literally >> what >> epsilon delta theorem says. This was learnt us already in 70Ēs in >> university. Are you back in 50's? > Which part of my statement do you not accept? Do you disagree with > the > definition I gave? >> Explained above. > Try again. You didn't mention any part of the definition, let alone say > which part you disagreed with. > Definition. Let { a_k } be a sequence and let L be a real number. > We say lim_{k->oo} a_k = L if, for every epsilon > 0, there exists > N > 0 such that | a_k - L | < epsilon for every k > N. > Remark 1. Exactly the same definition applies to standard analysis and > to nonstandard analysis, with the proviso that in NSA the epsilon > 0 > is allowed to be an infinitesimal and the N > 0 is allowed to be > infinitely large. >> Yes, agreed. > Remark 2. The definition does not say what it means for the limit to be > close to L. The definition only says what it means for the limit to be > equal to L. Either the definition is satisfied, or it isn't. >> OK. > Now, the questions: (1) Do you agree with the definition? (2) Do you > agree that according to this definition the limit is exactly 1, even in > NSA? If you don't agree, explain why not. >> Yes, I do agree as explained above in the cases 1 and 2. You did not >> consider at all the case 3 above. How does your definitions should be >> applied on the case 3? > There is no case 3 above. I don't know what you are talking about. >> You should also note that the limit is the upper boundary value. As you >> will >> see below, it's not the question about the limit but about AC and the >> point >> of reference as we construct the numbers integers, infinite integers, >> reals, >> hyperreals etc. > For example, try to give a > particular value of epsilon > 0 such that the definition is not > satisfied. Hint: choosing an infinitesimal epsilon is allowed, but it > won't help your case. The definition still works. >> What about case 3 above as you stop epsilons in standard part omitting >> non-standard part. > There is no case 3 above. I have explained that the sum over N is not > a sum in NSA, since N is not an internal set in NSA. That's why we sum > over *N instead. Because You don't see N as subset of *N. :-) >> I would like to ask the same from You. :-). Is it the point >> of reference that is strange concept for You? > Point of reference is an undefined concept and does not appear in the > definition of limit, quoted above. I won't comment on whether it is > strange, since things have to be defined first before they can > possibly > qualify as strange. >> The point of reference is counting point reference, which also separates >> infinities. > That is not a definition. For an example of what I mean by a definition, > look at my definition of what it means to say that lim_{k->oo} a_k = L. > Mathematical definitions leave no room for fuzzy language or vague > concepts. Try again. >> The standard point of reference is the normal decimal dot that separates >> the >> integer part and the decimal part, which can be infinite long string. >> Without the point of reference you do not know which part is integer part >> and which one is the decimal part. What ever you calculate you always >> refer >> your calculations to some point of reference. > The common definitions of the real numbers (via Dedekind cuts or Cauchy > sequences) do not mention decimal points at all and do not depend on > any such concepts as integer part and decimal part. For any real > number x, the integer part of x may be defined as floor(x) = max { n in > N : n <= x }. I had no need for any vague concepts such as point of > reference in writing that definition. Certainly not. It's alternative way to construct numbers from AC. The point of reference is in-constructed assumption in Dedekinds cut or Cauchy sequences, because they assumed so or they did not recognize the point of reference. >> In fact, there seems to be a slight conceptual difference in our >> argumentation. The difference is analocigally the same as we talk about >> finite decimal numbers. You accept that finite 0.99999 <1, as there are >> no >> infinite 9's. As hyperreals are omitted in the real limit counting (not >> counted over hyperreals), then in reals the limit equals to 1, i.e. >> 0.999...=1. But as hypereals exist, but omitted in the limit >> calculation, >> then 0,999...<1 in NSA. Simple as possible. Reals are finite from the >> hypereal point of view. Therefore 0.999...<1 - in hyperreals as only >> real >> area is considered. > You need to be precise about what you mean by 0.999... in NSA. I have > been taking it to mean the sum of 9/10^n for all n in *N, n > 0. You > evidently mean something different. In particular, it can't possibly > mean the sum over all finite values of n > 0, because that is not a set > in NSA. N is the subset of *N. I and You can count over subset of *N just like in the case of any subset of N. > But in NSA there is no such thing as a .999... that extends only through > finite digit positions. If the string is infinitely long, then it > necessarily extends to infinite digit positions in NSA. That may sound > vaguely similar to an argument commonly made by cranks, but the > difference is that the cranks are not talking about NSA. >> evidence. I >> used the case 3 as an example to point out how the people do not think as >> their argumentation contains hidden asumptions. So - if there exist >> non-standard part, which is purposely omitted, then you do not calculate >> the >> total or over-all limit. In this case you have to observe that there are >> numbers smaller than any real number and as a consequence 0.999... cannot >> be >> equal to 1, though the limit equals to 1. >> What is this paradox, which has been the reason to this thread, and how >> do >> we fix it? > If you do not sum 9/10^n for all n > 0, then you are not computing > 0.999.... The indicated sum is exactly 1. Shortly: That's what we have already agreed. I never denied that. What can be done: over N, over *N or over N as a subset of *N, and only in the last case the limit over N is smaller than 1 as You should count over *N in hyperreals. Therefore in principle 0.999... <1 in the last mentioned case. >> The solution is to point out that the limit is a mathematical upper >> boundary >> value, but does not tell the real value of the string but the next, i.e. >> successor, value of the string, because the limit calculation is based on >> the epsilon delta theorem. > The string I am talking about has no successor values. It's already > defined for all positions n, including the ones that are infinitely > large. > The definition of a limit in NSA may be stated in various ways, but > all > of them are equivalent to the usual epsilon-delta definition, with the > proviso that epsilons and deltas are allowed to be infinitesimal, and > N > is allowed to be infinitely large. >> Yes, that's what I mean - too, assuming we mean the same thing. If you >> limit >> your calculation into the real area and omit the hyperreal area, > You can't do that. That's the whole point. >> LetĒs demontrate it shortly now so simply as possible (like Donald Knuth >> 1) It is assumed that the digits [0,1...9] in 10-base system are >> constructed. I leave it for the home work. >> 2) Then we apply AC so that we have infinite many placeholders (or hooks) >> with the first one and the last one (the start and the end), just like in >> [0,1]. > We don't need AC here. We are defining d_0 = 0 and d_k = 9 for all k > 0 > in *N. >> (by the way this stops the discussion about the last digit in the >> infinite >> decimal string. :-)) For us it's enough that is just possible. > I was not aware that there was any such discussion. It was earlier and it arises up from time to time, but not in our mutual discussion. >> 3) Pick-up with the aid of AC some digits in every placeholder. > Again, AC is irrelevant. We already have our hyperinfinite string. >> What number do you have? Actually you have just digits, but not a >> number - >> yet. Why? > Because decimal digit strings are not numbers. They merely represent > numbers. >> Because you have not defined the point of reference! You have only digits >> in >> every place holder, i.e. in every hook. > Nonsense. If { d_k } is a decimal digit string, then the number > represented by the string is sum_{k in *N} d_k * 10^(-k). No point of > reference is needed. You cut (=snip) out the climax of my explanation. What does ^(-k) refer? Please answer to that simple question! Why minus - what does it refer? > [ snip nonsense about point of reference ] Your opinion, because You could not consider the successor of ...999. What is the successor of ...999 as all the placeholders are infinitely occupied with the maximal digit 9? Tapio > -- > Dave Seaman > Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. > === Subject: Re: .99999... still=/= 1 > It's necessary to observe: As the cardinality of reals R > cardinality of > integers N, so the cardinality of N_inf > N. As you count the limit > N --->oo instead of N-inf, then you certainly omit something - namely > hyperreal part. >> All very confused. Assuming you mean N_inf = *N, the set of >> hyperintegers, then it's true that *N as an external set has the >> cardinality of the reals, but the internal set *N has a *cardinality >> equal to *aleph_0. > This is of-course OK! >> This certainly doesn't mean that the hypernaturals >> are the same as transfinite cardinals. For one thing, there is a >> smallest transfinite cardinal (aleph_0), > Ok! >> but there is no such thing as a >> smallest infinite hypernatural. If n is an infinitely large integer, >> then so is n-1. > Omega was defined in this discussion earlier as follows: > The number that is greater than any infinite integer. That is the smallest > transinfinite number. Omega is the successor of ...999, i.e. n+1. The > precessor (n-1) of ...999 is ...998. It's possible to define the hyperordinals and to talk about *omega in NSA, but this *omega has no relation to anything you said in that paragraph. For one thing, *omega is not a member of *N. (In fact, *omega is identical to the set *N itself). For another, there is no connection between the hyperordinals and strings (even hyperstrings!) of decimal digits. I don't accept your definition. Are you under the impression that ...999 is a hyperinteger? It isn't, unless you explain which equivalence class of sequences of integers you are talking about. I can think of ways to make such a correspondence, but you haven't said what you mean. >> And none of this has anything to do with limits. You seem to think that >> infinity has only one meaning in all of mathematics. Wrong. > Your opinion. :-) Infinity has many meanings. It can refer to a compactification of the real line or of the complex plane, or to transfinite ordinals or cardinals, or to hyperreals, or to surreals. All of those are different. And this is not intended to be a complete list. > N (finite integers) does not cover hyperreal area, i.e. the numbers > smaller > than reals, because N hardly covers real area as discussed under the > thread > Are reals well-ordered. > As we count the real limit in NSA, then the hyperreals exist, but they > are > not counted in limit as N -->oo, but not as N_inf -->oo. Hyperreals are > omitted and therefore 0.999...<1 in hyperreals, though the real part of > the > limit equals to 1. >> I take it you mean the standard part of the limit is 1. > Well, we can talk about standard part and non-standard part, if you > prefer > this. >> I'm trying to guess what you might mean by the real part, since you >> have not defined your meaning. > the real part was the decimal part - as you certainly knew. No, I didn't know what you meant, and I still am not sure. What is the real part of sqrt(2), for example. It sounds like you trying to say the real part is sqrt(2) - 1, or approximately 0.41421. That was not one of my first two guesses. I would call that the fractional part. >> We are not talking about complex numbers >> here. > Exactly! That was my first guess, but my second guess was standard part. That is evidently not what you meant, either. In a similar fashion, you keep assuming that I must know what you mean by ...999. However, I assure you that I don't. > 2)Yes, the limit is exactly 1only if you count the limit including the > standard part as N --->oo. Then your reference set is N. >> Are you talking about standard analysis here, or nonstandard? > Standard analysis as You correctly observed. Then you are not discussing the value of 0.999... in NSA at all, as I previously thought. Looks like yet another example of miscommunication. Let's summarize: (1) We have 0.999... = 1 in standard analysis, because the sum is over N. (2) We have 0.999... = 1 in NSA, because the sum is over *N. (3) It is not possible to sum over *N in standard analysis, because *N is not a set in standard analysis. (4) It is not possible to sum over N in NSA, because N is not a set in NSA. Do you agree? >> The set N >> (consisting of the finite naturals) is not a set in the internal set >> theory of NSA. > Coorect, but it should be as *N is the extension of the set N. No, it should not be. There is an important principle involved, known as the transfer principle. This says that every theorem of standard analysis is also a theorem of NSA, provided we make the appropriate substitutions (such as substituting *N for each occurence of N). The transfer principle is extremely important. Without it, NSA loses most of its value as a tool of analysis. It turns out that if all sets in standard analysis are allowed to be internal sets in NSA, then we lose the transfer principle. That's why things are defined the way they are. >> Its counterpart is *N, which includes the infinitely >> large naturals. If you are forming a sum in NSA, then you can sum over >> *N, but not over N. > We can sum over subset too. Yes, but we can't sum over things that fail to be sets at all. That's the point. >> There is no case 3 above. I have explained that the sum over N is not >> a sum in NSA, since N is not an internal set in NSA. That's why we sum >> over *N instead. > Because You don't see N as subset of *N. :-) No, that is not the reason. The reason is that Abraham Robinson, the founder of NSA, did not see N as an internal set. And he had very good reasons. >> Nonsense. If { d_k } is a decimal digit string, then the number >> represented by the string is sum_{k in *N} d_k * 10^(-k). No point of >> reference is needed. > You cut (=snip) out the climax of my explanation. What does ^(-k) refer? > Please answer to that simple question! Why minus - what does it refer? The symbol ^ means that what follows is an exponent. Thus, 10^(-k) means ten to the power of (-k), which is the same as 1/10^k. We can write 0.999... as sum_{k=1}^oo 9*10^(-k) = sum_{k=1}^oo 9/10^k. >> [ snip nonsense about point of reference ] > Your opinion, because You could not consider the successor of ...999. What > is the successor of ...999 as all the placeholders are infinitely occupied > with the maximal digit 9? You haven't said what ...999 is. How am I supposed to answer questions about it if you don't define it? -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 (snip) > but there is no such thing as a > smallest infinite hypernatural. If n is an infinitely large integer, > then so is n-1. >> Omega was defined in this discussion earlier as follows: >> The number that is greater than any infinite integer. That is the >> smallest >> transinfinite number. Omega is the successor of ...999, i.e. n+1. The >> precessor (n-1) of ...999 is ...998. > It's possible to define the hyperordinals and to talk about *omega in > NSA, but this *omega has no relation to anything you said in that > paragraph. For one thing, *omega is not a member of *N. (In fact, > *omega is identical to the set *N itself). Correct, because that omega above (maybe some other name is better - let's use your symbol *w ?) is in the next infinite area. The reasons are: Every number has a successor, i.e. you can always add 1. All the placeholders in the infinite long area *N were already occupied. > For another, there is no > connection between the hyperordinals and strings (even hyperstrings!) of > decimal digits. I don't accept your definition. I could not follow you above, sorry. :-( > Are you under the impression that ...999 is a hyperinteger? It isn't, > unless you explain which equivalence class of sequences of integers you > are talking about. I can think of ways to make such a correspondence, > but you haven't said what you mean. OK, let's try again. First of all, I think we should start a new thread from the beginning so that everything is constructed and we use the same concepts and definitions. 1) ...999 is not N as it is not in a classic way finite integer. Let's call it infinite integer (N_inf) over one infinity. 2) I define it as I have done earlier sum (k 0 --> oo) 9*10^k. It does not have classic limit as the k refers now the standard point of reference, but it has a limit as you hopefully noticed as we have another point of reference. 3) It is defined and it exists, now - how do You like to name it? Hyperinteger or something else? (snip) > I'm trying to guess what you might mean by the real part, since you > have not defined your meaning. >> the real part was the decimal part - as you certainly knew. > No, I didn't know what you meant, and I still am not sure. What is the > real part of sqrt(2), for example. It sounds like you trying to say > the real part is sqrt(2) - 1, or approximately 0.41421. That was not > one of my first two guesses. I would call that the fractional part. Ok, that suits for me. (snip) > In a similar fashion, you keep assuming that I must know what you mean by > ...999. However, I assure you that I don't. Uh! I have tried to explain so simple as possible. I had once a fealing that You understood very well. There must be some miscommunication. >> 2)Yes, the limit is exactly 1only if you count the limit including the >> standard part as N --->oo. Then your reference set is N. > Are you talking about standard analysis here, or nonstandard? >> Standard analysis as You correctly observed. > Then you are not discussing the value of 0.999... in NSA at all, as I > previously thought. Looks like yet another example of miscommunication. > Let's summarize: > (1) We have 0.999... = 1 in standard analysis, because the > sum is over N. Yes, the limit is over N. I'm voluntary to point You that the sum and the limit are not the same thing. > (2) We have 0.999... = 1 in NSA, because the sum is over > *N. Yes, the limit is over *N. > (3) It is not possible to sum over *N in standard analysis, > because *N is not a set in standard analysis. Yes. I consider *N is the extension of N. > (4) It is not possible to sum over N in NSA, because N is > not a set in NSA. > Do you agree? I agree 1,2 and 3 but in the case 4 I disagree. Maybe we have to discuss about that topic more accurate. I consider finite integers are a subset of infinite integers over the first one infinity. > The set N > (consisting of the finite naturals) is not a set in the internal set > theory of NSA. >> Coorect, but it should be as *N is the extension of the set N. > No, it should not be. There is an important principle involved, known as > the transfer principle. This says that every theorem of standard > analysis is also a theorem of NSA, provided we make the appropriate > substitutions (such as substituting *N for each occurence of N). > The transfer principle is extremely important. Without it, NSA loses > most of its value as a tool of analysis. > It turns out that if all sets in standard analysis are allowed to be > internal sets in NSA, then we lose the transfer principle. That's why > things are defined the way they are. I cannot see where the transfer principle fails, except in the case of sum and limit. But in this case there are natural reasons as I have tried to explain. And the reason is not NSA. (snip) >> Your opinion, because You could not consider the successor of ...999. >> What >> is the successor of ...999 as all the placeholders are infinitely >> occupied >> with the maximal digit 9? > You haven't said what ...999 is. How am I supposed to answer questions > about it if you don't define it? I assume You can now answer after the definition - above. I propose anyway to start a new thread. Tapio > -- > Dave Seaman > Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. > === Subject: Re: .99999... still=/= 1 > (snip) >> but there is no such thing as a >> smallest infinite hypernatural. If n is an infinitely large integer, >> then so is n-1. > Omega was defined in this discussion earlier as follows: > The number that is greater than any infinite integer. That is the > smallest > transinfinite number. Omega is the successor of ...999, i.e. n+1. The > precessor (n-1) of ...999 is ...998. >> It's possible to define the hyperordinals and to talk about *omega in >> NSA, but this *omega has no relation to anything you said in that >> paragraph. For one thing, *omega is not a member of *N. (In fact, >> *omega is identical to the set *N itself). > Correct, because that omega above (maybe some other name is better - let's > use your symbol *w ?) is in the next infinite area. The reasons are: > Every number has a successor, i.e. you can always add 1. All the > placeholders in the infinite long area *N were already occupied. I don't know what you mean by an infinite area or by a placeholder. >> For another, there is no >> connection between the hyperordinals and strings (even hyperstrings!) of >> decimal digits. I don't accept your definition. > I could not follow you above, sorry. :-( >> Are you under the impression that ...999 is a hyperinteger? It isn't, >> unless you explain which equivalence class of sequences of integers you >> are talking about. I can think of ways to make such a correspondence, >> but you haven't said what you mean. > OK, let's try again. First of all, I think we should start a new thread from > the beginning so that everything is constructed and we use the same concepts > and definitions. > 1) ...999 is not N as it is not in a classic way finite integer. Let's call > it infinite integer (N_inf) over one infinity. As far as I am concerned, ...999 does not mean anything at all. It has no connection with NSA or anything else as far as I can see. You keep throwing that string around as if you think it has a meaning, but you have never said what that meaning is. I am not aware of any useful way of representing the members of *N as decimal digit strings. Any scheme I can think of suffers from one of two defects: either there are members of *N that don't fit into the naming scheme at all, or the coding scheme is so cryptic that you can't even compare the sizes of two numbers just by looking at the digits. Perhaps you can think of some scheme that I have overlooked, but you will have to define your terms very carefully before I will be convinced. > 2) I define it as I have done earlier sum (k 0 --> oo) 9*10^k. That sum diverges, even in NSA. It is not a number. > It does not > have classic limit as the k refers now the standard point of reference, but > it has a limit as you hopefully noticed as we have another point of > reference. There you go with your point of reference again. Sorry, but you can't use one undefined term to define another. > 3) It is defined and it exists, now - how do You like to name it? > Hyperinteger or something else? > (snip) It's a string of digits. Nothing more. It is not a number at all, at least in any sense that you have yet defined. And now, I would like to ask a counter-question. I will describe a certain member of *N, and I would like you to tell me what decimal digit string you think corresponds to it. First, some background. You may recall from other discussions that the (standard) real numbers can be defined as equivalence classes of Cauchy sequences of rationals. That means I can identify a real number by presenting you with a Cauchy sequence, and it is understood that any other sequence that happens to fall into the same equivalence class is an equally good representation of that number. For example, the sequences < 9/10, 99/100, 999/1000, ... > and < 1, 1, 1, 1, ... > happen to be two different representations of the same real number. Now, let's consider a similar construction that lies at the heart of nonstandard analysis. To describe a member of *N, for example, I can present you with a sequence of natural numbers (members of N). Unlike the real-number construction, this one doesn't require the sequences to be Cauchy. Technically, I also need to describe to you the equivalence relation that will be used, but that's a bit more complicated. It involves something called a free ultrafilter on N. You can find an explanation of the concept at . For our purposes, it's enough to know that if I give you a sequence in N, there is a unique member of *N that is represented by that sequence. Ok so far? Here is the sequence I have in mind. Let A(x,y) be the Ackermann Function, as described at . Now, let a_k = A(k,k) for each k. This sequence starts out: a_0 = A(0,0) = 1 a_1 = A(1,1) = 3 a_2 = A(2,2) = 7 a_3 = A(3,3) = 2^6 - 3 = 61 a_4 = A(4,4) = 2^2^2^2^2^2^2 - 3 = (too big to write out here) and after that the sequence starts to grow rather quickly. :-) Let a be the member of *N that is associated with this sequence. My question is: (1) what decimal digit string do you think represents a? (2) what decimal digit string do you think represents A(a,a)? My point is that your decimal digit strings are woefully inadequate in this context. They cannot even begin to describe the numbers in *N in any useful way. >> I'm trying to guess what you might mean by the real part, since you >> have not defined your meaning. > the real part was the decimal part - as you certainly knew. >> No, I didn't know what you meant, and I still am not sure. What is the >> real part of sqrt(2), for example. It sounds like you trying to say >> the real part is sqrt(2) - 1, or approximately 0.41421. That was not >> one of my first two guesses. I would call that the fractional part. > Ok, that suits for me. > (snip) >> In a similar fashion, you keep assuming that I must know what you mean by >> ...999. However, I assure you that I don't. > Uh! I have tried to explain so simple as possible. I had once a fealing that > You understood very well. > There must be some miscommunication. Answer my questions (1) and (2) above, and then we'll see whether there is any purpose at all in discussing decimal digit strings in connection with *N. >> (4) It is not possible to sum over N in NSA, because N is >> not a set in NSA. >> Do you agree? > I agree 1,2 and 3 but in the case 4 I disagree. Maybe we have to discuss > about that topic more accurate. I consider finite integers are a subset of > infinite integers over the first one infinity. Each of the finite naturals is a member of *N, but it does not follow from this that N is a subset of *N. That's part of why it's called nonstandard analysis. Not everything is a set in this model. >> The set N >> (consisting of the finite naturals) is not a set in the internal set >> theory of NSA. > Coorect, but it should be as *N is the extension of the set N. >> No, it should not be. There is an important principle involved, known as >> the transfer principle. This says that every theorem of standard >> analysis is also a theorem of NSA, provided we make the appropriate >> substitutions (such as substituting *N for each occurence of N). >> The transfer principle is extremely important. Without it, NSA loses >> most of its value as a tool of analysis. >> It turns out that if all sets in standard analysis are allowed to be >> internal sets in NSA, then we lose the transfer principle. That's why >> things are defined the way they are. > I cannot see where the transfer principle fails, except in the case of sum > and limit. But in this case there are natural reasons as I have tried to > explain. And the reason is not NSA. Let's consider the case of *R, for example. We know *R is the extension (the enlargement) of R. We also know that R satisfies the least upper bound property. By the transfer principle, *R must satisfy the least upper bound property. However, we also know that the collection R of finite reals is nonempty and is bounded above in *R by any infinitely large number. But R does not have a least upper bound in *R, because if x is infinitely large, then so is x-1. The conclusion is that R cannot be a set in NSA. The least upper bound principle is preserved because it applies only to nonempty *subsets* of *R that are bounded above, and R is not a *subset* at all. > (snip) > Your opinion, because You could not consider the successor of ...999. > What > is the successor of ...999 as all the placeholders are infinitely > occupied > with the maximal digit 9? >> You haven't said what ...999 is. How am I supposed to answer questions >> about it if you don't define it? > I assume You can now answer after the definition - above. I propose anyway > to start a new thread. You have not defined ...999. If you think you know what it is, then why don't you try answering your question and explaining your answer? -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 (snip) > I don't know what you mean by an infinite area or by a placeholder. Perhaps it does not help to read my emails carefully. :-( (snip) >> OK, let's try again. First of all, I think we should start a new thread >> from >> the beginning so that everything is constructed and we use the same >> concepts >> and definitions. >> 1) ...999 is not N as it is not in a classic way finite integer. Let's >> call >> it infinite integer (N_inf) over one infinity. > As far as I am concerned, ...999 does not mean anything at all. It has > no connection with NSA or anything else as far as I can see. You keep > throwing that string around as if you think it has a meaning, but you > have never said what that meaning is. If You and I can define it, as I have hopefully done, then there is a meaning and a connection to the existing mathematics! > I am not aware of any useful way of representing the members of *N as > decimal digit strings. Any scheme I can think of suffers from one of two > defects: either there are members of *N that don't fit into the naming > scheme at all, or the coding scheme is so cryptic that you can't even > compare the sizes of two numbers just by looking at the digits. It think there is now something misundertanding, of course I take the reason. *N is (infinite) integer part, what ever You like to call it. I have a feeling that we have to start from the premices. > Perhaps you can think of some scheme that I have overlooked, but you will > have to define your terms very carefully before I will be convinced. >> 2) I define it as I have done earlier sum (k 0 --> oo) 9*10^k. > That sum diverges, even in NSA. It is not a number. Yes, from Your point of view, because You have not recognized that this diverging sum indeed have a limit as You consider a new point of reference. As You or I write 9/10^-k or as I write 9*10^k, then k (as integer in N or *N) refers to some point of reference. Sorry, if this is so difficult. >> It does not >> have classic limit as the k refers now the standard point of reference, >> but >> it has a limit as you hopefully noticed as we have another point of >> reference. > There you go with your point of reference again. Sorry, but you can't > use one undefined term to define another. The point of reference is the counting point of reference. Everything is compared to some point of reference. >> 3) It is defined and it exists, now - how do You like to name it? >> Hyperinteger or something else? >> (snip) > It's a string of digits. Nothing more. It is not a number at all, at > least in any sense that you have yet defined. I assume, because You cannot see the limit? There is no number if there is no limit? Do You think so? > And now, I would like to ask a counter-question. I will describe a > certain member of *N, and I would like you to tell me what decimal digit > string you think corresponds to it. First, some background. > You may recall from other discussions that the (standard) real numbers > can be defined as equivalence classes of Cauchy sequences of rationals. > That means I can identify a real number by presenting you with a Cauchy > sequence, and it is understood that any other sequence that happens to > fall into the same equivalence class is an equally good representation of > that number. For example, the sequences > < 9/10, 99/100, 999/1000, ... > > and > < 1, 1, 1, 1, ... > > happen to be two different representations of the same real number. Yes, within the concept of the limit calculation. But that is not true (this is my point of argumentation, which I have to explain for You) the sum is not the same as the limit. The limit is the successor of the sum. As You do not - yet - accept my argumentation, I have to explain it more clear for You, though my personal opinion is that I have done it already. Sorry - this seems to be more complex that I expected. :-( > Now, let's consider a similar construction that lies at the heart of > nonstandard analysis. To describe a member of *N, for example, I can > present you with a sequence of natural numbers (members of N). Unlike > the real-number construction, this one doesn't require the sequences to > be Cauchy. Technically, I also need to describe to you the equivalence > relation that will be used, but that's a bit more complicated. It > involves something called a free ultrafilter on N. You can find an > explanation of the concept at > . I have a strong feeling that we are taking about much very more simpler things. Your ultrafilters are me very strange matter. I'm very sorry. :-( > For our purposes, it's enough to know that if I give you a sequence in N, > there is a unique member of *N that is represented by that sequence. Ok > so far? > Here is the sequence I have in mind. Let A(x,y) be the Ackermann > Function, as described at > . Now, let a_k = > A(k,k) for each k. This sequence starts out: > a_0 = A(0,0) = 1 > a_1 = A(1,1) = 3 > a_2 = A(2,2) = 7 > a_3 = A(3,3) = 2^6 - 3 = 61 > a_4 = A(4,4) = 2^2^2^2^2^2^2 - 3 = (too big to write out here) > and after that the sequence starts to grow rather quickly. :-) > Let a be the member of *N that is associated with this sequence. My > question is: > (1) what decimal digit string do you think represents a? > (2) what decimal digit string do you think represents A(a,a)? > My point is that your decimal digit strings are woefully inadequate in > this context. They cannot even begin to describe the numbers in *N in > any useful way. Huh! I'm indeed totaly out! Sorry. I have NOT descibed something so complicated like that. I cannot give You an answer. I assume we have now a very strange vision what I have told before. >> (snip) > In a similar fashion, you keep assuming that I must know what you mean > by > ...999. However, I assure you that I don't. >> Uh! I have tried to explain so simple as possible. I had once a fealing >> that >> You understood very well. >> There must be some miscommunication. > Answer my questions (1) and (2) above, and then we'll see whether there > is any purpose at all in discussing decimal digit strings in connection > with *N. The only possibility is to talk about limit of those expressions as we change the point of reference, but I cannot see Your goal. > (4) It is not possible to sum over N in NSA, because N is > not a set in NSA. > Do you agree? >> I agree 1,2 and 3 but in the case 4 I disagree. Maybe we have to discuss >> about that topic more accurate. I consider finite integers are a subset >> of >> infinite integers over the first one infinity. > Each of the finite naturals is a member of *N, but it does not follow > from this that N is a subset of *N. That's part of why it's called > nonstandard analysis. Not everything is a set in this model. ???? (snip) >> I cannot see where the transfer principle fails, except in the case of >> sum >> and limit. But in this case there are natural reasons as I have tried to >> explain. And the reason is not NSA. > Let's consider the case of *R, for example. We know *R is the extension > (the enlargement) of R. Yes, but You may have different vison? > We also know that R satisfies the least upper > bound property. Yes, as and if I consider the limit and the sum of the string. > By the transfer principle, *R must satisfy the least > upper bound property. As every limit. > However, we also know that the collection R of > finite reals is nonempty and is bounded above in *R by any infinitely > large number. Now You talk about reals with infinite integers and plus fractional part? > But R does not have a least upper bound in *R, because if > x is infinitely large, then so is x-1. No, because there is an exception. The limit of *R comes on or against at x+1 as all the placeholders were totaly occupied with the maximal digit within the choosen base system! > The conclusion is that R cannot > be a set in NSA. The least upper bound principle is preserved because it > applies only to nonempty *subsets* of *R that are bounded above, and R is > not a *subset* at all. Here our opinions needs further to discuss. :-) Tapio >> (snip) > -- > Dave Seaman > Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. > === Subject: Re: .99999... still=/= 1 >> I don't know what you mean by an infinite area or by a placeholder. > Perhaps it does not help to read my emails carefully. :-( I have not received any email from you. >> As far as I am concerned, ...999 does not mean anything at all. It has >> no connection with NSA or anything else as far as I can see. You keep >> throwing that string around as if you think it has a meaning, but you >> have never said what that meaning is. > If You and I can define it, as I have hopefully done, then there is a > meaning and a connection to the existing mathematics! You have not defined ...999 except to say that it means sum_n 9*10^n, which is nonsense. Are you forgetting the transfer principle? That sum diverges in standard analysis (summing for n in N), and therefore it also diverges in NSA (summing for n in *N). Sorry, but you have not defined anything. > It think there is now something misundertanding, of course I take the > reason. *N is (infinite) integer part, what ever You like to call it. I have > a feeling that we have to start from the premices. That's exactly what I did when I explained about equivalence classes of integer sequences. That's as basic as it gets in NSA. >> And now, I would like to ask a counter-question. I will describe a >> certain member of *N, and I would like you to tell me what decimal digit >> string you think corresponds to it. First, some background. >> You may recall from other discussions that the (standard) real numbers >> can be defined as equivalence classes of Cauchy sequences of rationals. >> That means I can identify a real number by presenting you with a Cauchy >> sequence, and it is understood that any other sequence that happens to >> fall into the same equivalence class is an equally good representation of >> that number. For example, the sequences >> < 9/10, 99/100, 999/1000, ... > >> and >> < 1, 1, 1, 1, ... > >> happen to be two different representations of the same real number. > Yes, within the concept of the limit calculation. But that is not true (this > is my point of argumentation, which I have to explain for You) the sum is > not the same as the limit. The limit is the successor of the sum. As You do > not - yet - accept my argumentation, I have to explain it more clear for > You, though my personal opinion is that I have done it already. Sorry - this > seems to be more complex that I expected. :-( >> Now, let's consider a similar construction that lies at the heart of >> nonstandard analysis. To describe a member of *N, for example, I can >> present you with a sequence of natural numbers (members of N). Unlike >> the real-number construction, this one doesn't require the sequences to >> be Cauchy. Technically, I also need to describe to you the equivalence >> relation that will be used, but that's a bit more complicated. It >> involves something called a free ultrafilter on N. You can find an >> explanation of the concept at >> . > I have a strong feeling that we are taking about much very more simpler > things. Your ultrafilters are me very strange matter. I'm very sorry. :-( As I explained, you don't need to know what an ultrafilter is in order to grasp the basic point of the example. We have a hyperinteger, a member of *N, that is described by a particular sequence. By the way, since the terms of the sequence are unbounded, we can conclude that the associated hyperinteger is infinitely large. >> For our purposes, it's enough to know that if I give you a sequence in N, >> there is a unique member of *N that is represented by that sequence. Ok >> so far? >> Here is the sequence I have in mind. Let A(x,y) be the Ackermann >> Function, as described at >> . Now, let a_k = >> A(k,k) for each k. This sequence starts out: >> a_0 = A(0,0) = 1 >> a_1 = A(1,1) = 3 >> a_2 = A(2,2) = 7 >> a_3 = A(3,3) = 2^6 - 3 = 61 >> a_4 = A(4,4) = 2^2^2^2^2^2^2 - 3 = (too big to write out here) >> and after that the sequence starts to grow rather quickly. :-) >> Let a be the member of *N that is associated with this sequence. My >> question is: >> (1) what decimal digit string do you think represents a? >> (2) what decimal digit string do you think represents A(a,a)? >> My point is that your decimal digit strings are woefully inadequate in >> this context. They cannot even begin to describe the numbers in *N in >> any useful way. > Huh! I'm indeed totaly out! Sorry. I have NOT descibed something so > complicated like that. I cannot give You an answer. I assume we have now a > very strange vision what I have told before. That's the very point I was trying to make. You have been talking about infinite strings of digits, under the mistaken impression that you were talking about hyperintegers. The whole point of my description above was to show that hyperintegers are not even remotely like what you thought they were. Your decimal digit strings are most certainly not hyperintegers. As far as I can see, your digit strings are not numbers, they have no interesting properties, and they are not worth discussing at all. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 > LEARN MATH. His math is sound. Yours is non-existent. Bob Kolker === Subject: Re: .99999... still=/= 1 In sci.math, robert j. kolker : >> LEARN MATH. > His math is sound. Yours is non-existent. the non-standard analysis arena, an area which is not all that familiar to me except as a crudely expressed d-math, which I can occasionally use (how correctly, I've no idea!) to expound on various concepts. It's clear that his definition of '=' is a bit different from the rest of ours, and limit theory has some problems. For example, take .999..., the much-balleyhooed expression. Express it as the series: S_1 = .9 S_2 = .9 + .09 S_3 = .9 + .09 + .009 ... S_n = sum(i=1,n) (9 * 10^(-i)) = 1 - 10^(-n) (easily proved by induction, if one cares to bother). More or less standard stuff, up to this point. Under normal circumstances one can play the N-epsilon [*] game and get the following proof (or outline thereof). Oh, you have an epsilon > 0 for me? Fine, I'll take N = ceil(log10(1/epsilon)). I can now prove that, for any n > N, S_n > 1 - epsilon, but less than 1. Since S_n = 1 - 10^(-n), if n > N, then 10^(-n) < 10^(-ceil(log10(1/epsilon))) <= 10^(-log10(1/epsilon)) <= epsilon. and then the jump: Hence, lim(n->+oo) S_n = 1. QED. Now enter hypperreals. Set epsilon = d, where d is a number greater than 0 but less than all 1/n, n > 0, n in J. This proof goes out the window, as 1/d is a meaningless expression (though one could generate another class of numbers, maybe called quasi-infinities, which would be greater than any integer N but less than aleph_0, or something equally strange; the main intent is to be dual to the hyperreals). One could claim 'd' is a ridiculous concept (and it is to some extent as lim(n->+oo) (1/n) = 0 anyway, in standard analysis), but it does lead to some interesting questions as to how to get around this obstacle without simply claiming well, it's obviously nonsense or well, we've always done it that way. It's a bit like Lobachevskian geometry in that respect -- not a contradiction, but a new realm of number. Not a horribly useful one, to be sure -- 21 or so digits of pi or e are enough to define the Earth's orbit (1.5 * 10^11 m) to the width of an atom (2 * 10^-10 m); the rest is gravy -- but interesting to some, and useful for testing microprocessors. This is not to say S. Enterprize's arguments are any good; they're extremely sloppy, in fact. > Bob Kolker [*] there are four variants of this game (each with three or nine subvariants), depending on what one is proving. delta-epsilon: lim(x->a) f(x) = b lim(x->a+) f(x) = b lim(x->a-) f(x) = b N-epsilon: lim(x->oo) f(x) = b lim(x->+oo) f(x) = b lim(x->-oo) f(x) = b delta-M: lim(x->a) f(x) = oo (or +oo or -oo) lim(x->a+) f(x) = oo (or +oo or -oo) lim(x->a-) f(x) = oo (or +oo or -oo) N-M: lim(x->oo) f(x) = oo (or +oo or -oo) lim(x->+oo) f(x) = oo (or +oo or -oo) lim(x->-oo) f(x) = oo (or +oo or -oo) -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 > Under normal circumstances one can play the N-epsilon [*] game > and get the following proof (or outline thereof). > Oh, you have an epsilon > 0 for me? Fine, I'll take > N = ceil(log10(1/epsilon)). I can now prove that, > for any n > N, S_n > 1 - epsilon, but less than 1. > Since S_n = 1 - 10^(-n), if n > N, then > 10^(-n) < 10^(-ceil(log10(1/epsilon))) > <= 10^(-log10(1/epsilon)) <= epsilon. > and then the jump: > Hence, lim(n->+oo) S_n = 1. QED. > Now enter hypperreals. Set epsilon = d, where d is > a number greater than 0 but less than all 1/n, n > 0, n in J. > This proof goes out the window, as 1/d is a meaningless > expression (though one could generate another class of > numbers, maybe called quasi-infinities, which would be > greater than any integer N but less than aleph_0, or something > equally strange; the main intent is to be dual to the hyperreals). Actually, the hyperreals *R form a field. Yes, 1/d is infinitely large if d is an infinitesimal. Also, it should be noted that you can use the standard definition for the limit of a sequence: Definition. Let { a_k } be a sequence and L in R. Then we say that lim_{k->oo} a_k = L if, for every epsilon > 0, there exists N > 0 such that | a_k - L | < epsilon for every k > N. The only difference is in the interpretation of that the terms mean. In nonstandard analysis (NSA), when we say for every epsilon > 0, we mean for every positive epsilon in *R, which means epsilon is allowed to be an infinitesimal, for example. And when we say there exists N > 0 we mean that N is allowed to be infinitely large. It's a theorem of NSA that the following two statements are equivalent: (1) lim_{k->oo} a_k = L (as defined above), and (2) The difference | a_k - L | is an infinitesimal whenever k is infinitely large. Oh, and by the way, it's also true in NSA that sum_{n in *N, n >0} 9/10^n = 1. It's a geometric series. Thus we can say .999... = 1, even in the hyperreals. And no, it's not possible to confine the sum to just the finite digit positions, because the summation can only be carried out over a set, and the finite naturals are not a set according to the internal set theory of NSA. When we say something is infinitely large in NSA, that's only the external view. Within the model, all the members of *R are finite. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: .99999... still=/= 1 In sci.math, Dave Seaman : >> Under normal circumstances one can play the N-epsilon [*] game >> and get the following proof (or outline thereof). >> Oh, you have an epsilon > 0 for me? Fine, I'll take >> N = ceil(log10(1/epsilon)). I can now prove that, >> for any n > N, S_n > 1 - epsilon, but less than 1. >> Since S_n = 1 - 10^(-n), if n > N, then >> 10^(-n) < 10^(-ceil(log10(1/epsilon))) >> <= 10^(-log10(1/epsilon)) <= epsilon. >> and then the jump: >> Hence, lim(n->+oo) S_n = 1. QED. >> Now enter hypperreals. Set epsilon = d, where d is >> a number greater than 0 but less than all 1/n, n > 0, n in J. >> This proof goes out the window, as 1/d is a meaningless >> expression (though one could generate another class of >> numbers, maybe called quasi-infinities, which would be >> greater than any integer N but less than aleph_0, or something >> equally strange; the main intent is to be dual to the hyperreals). > Actually, the hyperreals *R form a field. Yes, 1/d is infinitely large > if d is an infinitesimal. Also, it should be noted that you can use the > standard definition for the limit of a sequence: > Definition. Let { a_k } be a sequence and L in R. > Then we say that lim_{k->oo} a_k = L if, for every epsilon > 0, there > exists N > 0 such that | a_k - L | < epsilon for every k > N. > The only difference is in the interpretation of that the terms mean. In > nonstandard analysis (NSA), when we say for every epsilon > 0, we mean > for every positive epsilon in *R, which means epsilon is allowed to be > an infinitesimal, for example. And when we say there exists N > 0 we > mean that N is allowed to be infinitely large. > It's a theorem of NSA that the following two statements are equivalent: > (1) lim_{k->oo} a_k = L (as defined above), and > (2) The difference | a_k - L | is an infinitesimal whenever k is > infinitely large. > Oh, and by the way, it's also true in NSA that sum_{n in *N, n >0} 9/10^n >= 1. It's a geometric series. Thus we can say .999... = 1, even in the > hyperreals. > And no, it's not possible to confine the sum to just the finite digit > positions, because the summation can only be carried out over a set, and > the finite naturals are not a set according to the internal set theory of > NSA. When we say something is infinitely large in NSA, that's only the > external view. Within the model, all the members of *R are finite. Interesting. So even in the hyperreals, S. Enterprize is simply wrong. :-) -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: .99999... still=/= 1 > Interesting. So even in the hyperreals, S. Enterprize is simply wrong. :-) I told you. Bob Kolker === Subject: Re: .99999... still=/= 1 >> Interesting. So even in the hyperreals, S. Enterprize is simply wrong. :-) >I told you. >Bob Kolker .999... < 1 x is said to be infinitesimal iff |x| < 1/n for all integers n. http://mathworld.wolfram.com/HyperrealNumber.html Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > x is said to be infinitesimal iff |x| < 1/n for all integers n. By the transfer principle the limit of the partial sums still is 1. Bob Kolker === Subject: Re: .99999... still=/= 1 >> x is said to be infinitesimal iff |x| < 1/n for all integers n. >By the transfer principle the limit of the partial sums still is 1. >Bob Kolker Does this converge to ? .0000000000000000000000...1... Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > > x is said to be infinitesimal iff |x| < 1/n for all integers n. >>By the transfer principle the limit of the partial sums still is 1. >>Bob Kolker > Does this converge to ? >.0000000000000000000000...1... And what about this, what does this converge to? SUM 9/10^i... = ? Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > And what about this, what does this converge to? The SUM is a limit it does not converge to anything. It is the -sequence- of partial sums that does the converging. > SUM 9/10^i... = ? 1.0 of course. The same as for the standard reals, assuming that the sum is over the finite integers. Bob Kolker === Subject: Re: .99999... still=/= 1 >> >> x is said to be infinitesimal iff |x| < 1/n for all integers n. >By the transfer principle the limit of the partial sums still is 1. >Bob Kolker Reference LINK http://www.users.bigpond.com/pidro/counter-examplestoFLT1.htm quote from LINK: 4. CRITIQUE OF THE REALS We summarize the defects of the reals identified in [10, 13, 14, 17, 18, 19]: (1) the role of the axiom of choice or its variants; (2) the ill-defining of the nonterminating decimals; (3) lack of validity of the dichotomy axiom [3, pp. 52 [CapitalEth] 6-]; (4) unsolved problem of natural ordering; and (5) limitation of domain of the additive and multiplicative operations to terminating decimals. The last one is rather startling but this example illustrates this point: Compute (1.999.83)/2. With standard computation this algorithm never stops and the answer is never found. In practice, the computer calculates to the limit of its capacity and prints out a terminating decimal of the form 0.999.839 as the supposed answer, which is wrong. Moreover, that answer would contradict a theorem in the reals which says: let x, y be reals such that x < y; then x < (x+y)/2 < y. Taking x = 1, y = 0.999.83, we have, 0.999.839 less than y alright but also less than x, contradicting the theorem. One may argue that 1 = 0.999.83 to evade this contradiction. However, present construction of the reals has no proof of this statement, mainly, because 0.999.83 is ill-defined and does not belong to the domain of the additive and multiplicative operations. Moreover, in the natural ordering of the decimals, we have 0.999.83 < 1 [13]. Therefore, since some nonzero reals, terminating or nonterminating, do not have multiplicative inverse in this domain, it follows that this so-called complete ordered field is, after all, neither complete, nor ordered nor a field (see dialogue in [13]). See I told you, .999... < 1 So, .999... =/= 1 Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 >> >> x is said to be infinitesimal iff |x| < 1/n for all integers n. > >By the transfer principle the limit of the partial sums still is 1. > >Bob Kolker > > Reference LINK > http://www.users.bigpond.com/pidro/counter-examplestoFLT1.htm > quote from LINK: > 4. CRITIQUE OF THE REALS You have chosen another well-known crackpot as your expert source. Congratulations. EEE is currently contributing to this newsgroup, if you want to read more of his ramblings. - Randy === Subject: Re: .99999... still=/= 1 >> >x is said to be infinitesimal iff |x| < 1/n for all integers n. >> >>By the transfer principle the limit of the partial sums still is 1. >> >>Bob Kolker >> > Reference LINK > http://www.users.bigpond.com/pidro/counter-examplestoFLT1.htm > quote from LINK: > 4. CRITIQUE OF THE REALS > We summarize the defects of the reals identified in [10, 13, 14, 17, 18, 19]: > (1) the role of the axiom of choice or its variants; (2) the ill-defining of > the nonterminating decimals; (3) lack of validity of the dichotomy axiom [3, > pp. 52 [CapitalEth] 6-]; (4) unsolved problem of natural ordering; and (5) limitation of > domain of the additive and multiplicative operations to terminating decimals. > The last one is rather startling but this example illustrates this point: > Compute (1.999.83)/2. With standard computation this algorithm never stops and > the answer is never found. In practice, the computer calculates to the limit of > its capacity and prints out a terminating decimal of the form 0.999.839 as the > supposed answer, which is wrong. Moreover, that answer would contradict a > theorem in the reals which says: let x, y be reals such that x < y; then x < > (x+y)/2 < y. Taking x = 1, y = 0.999.83, we have, 0.999.839 less than y alright > but also less than x, contradicting the theorem. One may argue that 1 = > 0.999.83 to evade this contradiction. However, present construction of the > reals has no proof of this statement, mainly, because 0.999.83 is ill-defined > and does not belong to the domain of the additive and multiplicative > operations. Moreover, in the natural ordering of the decimals, we have 0.999.83 > < 1 [13]. Therefore, since some nonzero reals, terminating or nonterminating, > do not have multiplicative inverse in this domain, it follows that this > so-called complete ordered field is, after all, neither complete, nor ordered > nor a field (see dialogue in [13]). Bob Kolker === Subject: Re: .99999... still=/= 1 > This is not to say S. Enterprize's arguments are any good; > they're extremely sloppy, in fact. His arguments are not even wrong. They are non-existent. Stringing words together doth not an argument make. Bob Kolker === Subject: Re: .99999... still=/= 1 >> This is not to say S. Enterprize's arguments are any good; >> they're extremely sloppy, in fact. >His arguments are not even wrong. They are non-existent. Stringing words >together doth not an argument make. >Bob Kolker Thou shouldth have understandeth by nowth. Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > They don't have a disagreement about anything mathematical. It should > be clear by now that SE is not arguing in good faith, but is just > trolling. Bob Kolker === Subject: Re: .99999... still=/= 1 >> They don't have a disagreement about anything mathematical. It should >> be clear by now that SE is not arguing in good faith, but is just >> trolling. >Bob Kolker If you notice they still haven't proven, .999...(an unreal number) = 1 ( a real number). Smart's Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813&cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: .99999... still=/= 1 > If you notice they still haven't proven, > .999...(an unreal number) = 1 ( a real number). Meaningless. This is not a mathematical experession. Bob Kolker === Subject: Re: Proof of Sum_{i=1...n} i^k is a polynomial expression over n by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHFa5n05215; >Say S_k(n) = Sum_{i=1...n} i^k = 1^k + 2^k + .... + n^k. >I want to prove that S_k(n) is a polynomial expression over n, that >is, that there exists a polynomial p_k(x) in R[x] such that S_k(n) = >p_k(n) for all n (and p_k only depends of k). >I prefer proofs by induction and elementals. I know that it could be >proved using the Bernoulli polynomials, but I want a proof without >that (I want more elemental proof). Could it be?. I tried but I did >not get it. >Xan. N.94 H.89o Xan, 'non-polynomial differential ' could help you. In fact sum(n=1 to n=x n^k ) verifies the following simple equation: p(x)-p(x-1)=x^k or (I-exp(-D))Įp(x)=x^k or p(x)=I/(I-exp(-D))Įx^k . For program reason we must enter:instead of x^k x^(k+1)/(k+1) The given formula corresponds to a polyniomial. === Subject: Re: .99999... still=/= 1 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHFa5005223; >Dedekind is credited with giving the first mathematical definition >of the real numbers. >> Is this so? >Yes and no. The set of real numbers was implicitly defined by >algebraic laws on the two basic operations + and *. A rigorous >definition (or reduction) of real numbers to the rationals was done in >the latter half of the 19-th century along with definitions of >continuous functions, differentiable functions and limits. The key to >the whole business is the rigorous definition of limit. >The reals are the topological closure of the rationals. The key to this >is a definition of convergence in which a limit is not explicitly >required. This is attributed to Cauchy. >Bob Kolker I believe you mean topological _completion_, rather than closuer. - MO === Subject: Re: .99999... still=/= 1 > I believe you mean topological _completion_, rather than closuer. Quite so. Dediking and Cauchy found a way of adding the limit points to the set of rationals. Bob Kolker === Subject: Parameter Estimamtion of a Exponential Dist. P(x)=1/A exp(-x/A) is known as an exponential distribution, where Mean=A and Variance=A*A. Using Maximum Likelihood Method, A'=(Sample Mean) can be found. However, I plan to use A'=sqrt(Sample Variance). Does any one have an idea about the robustness of the estimation ? === Subject: Re: Parameter Estimamtion of a Exponential Dist. > However, I plan to use A'=sqrt(Sample Variance). Does any one have > an idea about the robustness of the estimation ? Sample variance is a biased estimator of population variance: = A^2 (n-1) / n. I can prove that A' is a biased estimator of A, but haven't been able to derive a closed expression for /A in terms of n. Unfortunately, setting A' = sqrt(Sample Variance * n / (n-1)) does not remove the bias. - Tim === Subject: Re: weighted arithmetic and geometric means by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBHFxcn07339; >Hello >Suppose x_1,....x_n and w_1,...w_n are postive numbers and define >a = (Sum(i=1,n)(w_i*x_i))/(Sum(i=1,n)(w_i)) and >g = (Product(i=1,n)(x_i)^(w_i))^(1/Sum(i=1,n)(w_i))) >I want to prove that there holds an inequalty similar to that related >to the arithmetic and geometric means, that is, a>= g, with equality >if, and only if, x_1 = ....x_n. >Since I already now that the arithmetic/geometric means inequalty is >true, I tried to do as follows. >First, if all the w_i's are positive integers, then we see readily see >that a is the arithmetic mean of numbers x_1,...x_n if if we we take >each x_i w_i times. Since a similar conclusion is true of g, we apply >the a/g means inequality to conclude that, if all the w_i's are >integer then the propostion is true for a and g. >If all the w_i's are rational, then, representing each w_i as the >ratio between 2 positive integers and doing some elementary algebraic >transformations, we see a =a' and g =g', where a' and g' are weighted >means similar to a and g corresponding, now, to integer weights. >Therefore, we are sent back to the integer case, which shows the >proposition still holds if all the w_i's are positive rationals. >If the w_i's are real positive integers, then, for a fixed but >arbitray (x_1,...x_n) , the functions (w_1,...w_n) -> a(w_1,...w_n) >and (w_1,...w_n) -> g(w_1,...w_n,)defined on the subset of R^n >composed of their points with positive coordinates, are continuous. >Since a>=g in the subset of R^n composed of their points with >positive and rational coordinates and since this latter subset is >dense in the former, it follows that a(w_1,...w_n) >= g(w_1,...w_n) >for every positive w_1,...w_n. Since this holds for arbitray positive >x_1,...x_n, we have proved that, in fact, a>=g. But we are not done, >because these arguments do not imply that equality occurs if and only >if x_1...= x_n. >Following my reasoning, can anyone suggest how I can complete the >proof? Or, maybe, it's better to start at the very beginning, without >supposing the a/g means inequalty is known. >Amanda The classical reference for these sorts of inequalities is (amazingly entitled) _Inequalities_, by Hardy, Littlewood, & Polya. Chapters 1 and 2 are all(!) you need. Nick === Subject: Question about President's Social Security plan by the amount of $2.7 trillion in 75 years. Bush administration has a plan. The plan is to privatize some parts of social security. This will cost $2 trillion to set up. It is not guaranteed to fix things, but is only one part of an integrated plan. So my question is, wouldn't it make more sense to just GIVE that $2 trillion to social security, which is guaranteed to fix things by exactly $2 trillion, just leaving a small $0.7 trillion shortfall after 75 years? === Subject: Re: Question about President's Social Security plan >by the amount of $2.7 trillion in 75 years. >Bush administration has a plan. The plan is >to privatize some parts of social security. >This will cost $2 trillion to set up. >It is not guaranteed to fix things, but >is only one part of an integrated plan. >So my question is, wouldn't it make more >sense to just GIVE that $2 trillion to >social security, which is guaranteed >to fix things by exactly $2 trillion, just >leaving a small $0.7 trillion shortfall after >75 years? You mean other then this train wreck if the media ever made this information Public?! I mean name me just ONE Democrat that would still be left in office if the public found out that they had been lied to and that the Social Security funds were being stolen by the Democrats for the last 60+ years? Here are the REAL facts Social Security.89s vaunted trust fund doesn.89t exist; taxes paid into Social Security are merely being handed over as benefits to other people. On May 2nd, President Bush announced the formation of a presidential commission to deal with the Social Security crisis. The last such commission, in 1983, had as its chairman Alan Greenspan. It recommended enormous increases in taxes, and Congress dutifully complied.Government spokesmen immediately patted themselves on their backs for having saved Social security. We are likely in for more of the same. The new commission.89s name is the Commission to Strengthen Social Security. That can only mean more taxes. The Bush administration, though, should not be trying to save Social Security. For decades americans have been deceived by this program, believing that their Social Security taxes are pouring into a fund set aside expressly for the purpose of old age insurance for the support of the elderly. This is a colossal lie and it is nothing short of scandalous. The truth is, the vaunted Social Security trust fund does not exist. Never has, never will. Haven.89t we been told for decades that the government scrupulously, almost religiously, maintains the Social Security trust fund? For the truth, we have to go back to 1935, shortly after the creation of Social Security. A man named George P. Davis contested the program in court, claiming that taxation to support it was unconstitutional, trampled on states.89 rights, and imposed an unjust monetary burden on firms in which he had invested. A federal court rejected his claims, but he won a favorable ruling from the First Circuit Court of Appeals in Boston. Had that Appeals Court decision remained in force, the entire Social Security Act would have been voided at the outset. As expected, however, the federal government.89s Commissioner of Internal Revenue, Guy T. Helvering, immediately appealed the matter to the Supreme Court. Lawyers for Mr. Davis contended that Social Security taxes were collected for a particular purpose (for unemployed and older Americans) and not for the constitutionally acceptable purpose of acquiring revenue for the general welfare of the nation as a whole. They also contended that the tax was not a constitutionally allowable excise tax, a type of taxation defined of use or consumption, not a tax on wages. In Helvering v. Davis, the Supreme Court.89s decision made reference to a related case wherein the court had tortuously maintained that the tax was indeed an excise tax and therefore legitimate. But the Court also agreed with the government.89s lawyers who had openly stated that social security taxes were not collected for a particular purpose but are paid into the Treasury as internal revenue collections, available for the general support of the government. That contention, forming the government.89s major argument against the claims by Mr. Davis, received official endorsement when the Supreme Court ruled in Helvering that the proceeds of the unemployment and old-age taxes are to be paid into the Treasury like internal- revenue taxes generally, and are not earmarked in any way. (Emphasis added.) This decision has never been overturned. All talk about the social security trust fund containing social security tax revenue is pure, unadulterated blather. In 1975, former Secretary of Commerce and former Director of the Budget Maurice Stans hit the nail on the head when he stated: Social Security payments rest upon the general credit of the Government of the United States, upon its taxing power, and not upon any accumulations in a trust fund. In 1976, then-Secretary of the contributors to the system have not been building a fund at all. The taxes they are paying into Social Security are merely being handed over as benefits to other people. In other words, Social Security is a huge Ponzi scheme. So, what the Bush administration is trying to do through the new Commission to Strengthen Social Security is to buttress a lie. The commission will surely attract more attention as it continues recommending placebos to treat a disease that will eventually prove fatal if not properly addressed. What should be done is really quite simple: Phase Social Security out. Allow freedom of choice and watch how few young Americans will stick with Social security. Programs doing precisely this have already been implemented in Chile and elsewhere with stunningly beneficial results. Once the people of Chile were given the choice in 1981, they opted out, put their money into private programs, saw those funds spark an economic surge that became the envy of all of Latin America, and destroyed much of their nation.89s harmful government paternalism. But America.89s leaders continue to insist that Social Security is a success and that only careful management of its trust funds is needed to insure its viability. In his 1975 book Social Security: The Fraud in Your Future, author Warren Shore concluded that claims about the existence of trust funds are made because they help foster the public notion that Social Security is like insurance with its premium pools [available] to support promises made. But the public has been misled. Sad to say, the current activity in Washington shows no signs of addressing this fraud. Go to http://www.ssa.gov and then do a search on Helvering v Davis and be amazed at the over 1000 different links that this case is brought up. NOW do you see why the Democrats are so terrified about this SS reform? They would be hanged and drawn'n'quartered if the seniors ever found out that they were stealing from them. The Democrats would never be elected to dog warden ever again if this was made public, and part of the reform is to MAKE THIS PUBLIC! You Democrats are staring down the barrel of a loaded gun in your own hands, and for some reason your pulling the trigger..... === Subject: Re: Question about President's Social Security plan >..... > In 1975, former Secretary of Commerce and former Director of the > Budget Maurice Stans hit the nail on the head when he stated: Social > Security payments rest upon the general credit of the Government of > the United States, upon its taxing power, and not upon any > accumulations in a trust fund. In 1976, then-Secretary of the > contributors to the system have not been building a fund at all. The > taxes they are paying into Social Security are merely being > handed over as benefits to other people. In other words, Social > Security is a huge Ponzi scheme. Exactly right. Social security is a tax collected and used by the government. The real problem is not the solevency of Social Security : it is the government budget deficit. However, being unable or unwilling to confront the long term budget deficit problem, W Bush and his republican cohorts find it more expedient to engineer and try to tackle the real problem of Social security. Fix the budget deficit (ie. balance the books of the government) and the social security crisis will disappear overnight! === Subject: Re: Question about President's Social Security plan <8ngbs05g00gg1bkqo94fjun6kq0rg8kumr@4ax.com> According to the SS trustees your claim is in error Long-Range Results Under the intermediate assumptions the combined OASI and DI Trust Funds are projected to become exhausted in 2042. For the 75-year projection period, the actuarial deficit is 1.89 percent of taxable payroll, 0.03 percentage point smaller than in last year's report. The open group unfunded obligation for OASDI over the 75-year period is $3.7 trillion in present value, $0.2 trillion more than the obligation estimated a year ago. The OASDI annual cost rate is projected to increase from 11.07 percent percent in 2078, or to a level that is 5.91 percent of taxable payroll more than the projected income rate for 2078. Expressed in relation to the projected gross domestic product (GDP), OASDI cost is estimated to rise from the current level of 4.3 percent of GDP, to 6.3 percent in 2030, and to 6.6 percent in 2078. Between about 2010 and 2030, OASDI cost will increase rapidly due to the retirement of the large baby-boom generation. After 2030, increases in life expectancy and relatively low fertility rates will continue to increase Social Security system costs, but more slowly. Annual cost will exceed tax income starting in 2018 at which time the annual gap will be covered with cash from redeeming special obligations of the Treasury, until these assets are exhausted in 2042. Separately, the DI fund is projected to be exhausted in 2029 and the OASI fund in 2044. Solvency The combined OASDI Trust Funds are projected to become insolvent (i.e., unable to pay scheduled benefits in full on a timely basis) when assets are exhausted in 2042 under the long-range intermediate assumptions. For the trust funds to remain solvent throughout the 75-year projection period, the combined payroll tax rate could be increased during the period in a manner equivalent to an immediate and permanent increase of 1.89 percentage points, benefits could be reduced during the period in a manner equivalent to an immediate and permanent reduction of 12.6 percent, general revenue transfers equivalent to $3.7 trillion (in present value) could be made during the period, or some combination of approaches could be adopted. Significantly larger changes would be required to maintain solvency beyond 75 years. http://www.ssa.gov/OACT/TR/TR04/II_highlights.html#wp76455 T.Carr === Subject: Re: Question about President's Social Security plan >According to the SS trustees your claim is in error It's pointless to read further. Basing a Social Security discussion on a Trust Fund frame is pure nonsense. Mason C >Long-Range Results >Under the intermediate assumptions the combined OASI and DI Trust Funds >are projected to become exhausted in 2042. For the 75-year projection >period, the actuarial deficit is 1.89 percent of taxable payroll, 0.03 >percentage point smaller than in last year's report. The open group >unfunded obligation for OASDI over the 75-year period is $3.7 trillion >in present value, $0.2 trillion more than the obligation estimated a >year ago. >The OASDI annual cost rate is projected to increase from 11.07 percent >percent in 2078, or to a level that is 5.91 percent of taxable payroll >more than the projected income rate for 2078. Expressed in relation to >the projected gross domestic product (GDP), OASDI cost is estimated to >rise from the current level of 4.3 percent of GDP, to 6.3 percent in >2030, and to 6.6 percent in 2078. >Between about 2010 and 2030, OASDI cost will increase rapidly due to >the retirement of the large baby-boom generation. After 2030, increases >in life expectancy and relatively low fertility rates will continue to >increase Social Security system costs, but more slowly. Annual cost >will exceed tax income starting in 2018 at which time the annual gap >will be covered with cash from redeeming special obligations of the >Treasury, until these assets are exhausted in 2042. Separately, the DI >fund is projected to be exhausted in 2029 and the OASI fund in 2044. >Solvency >The combined OASDI Trust Funds are projected to become insolvent (i.e., >unable to pay scheduled benefits in full on a timely basis) when assets >are exhausted in 2042 under the long-range intermediate assumptions. >For the trust funds to remain solvent throughout the 75-year projection >period, the combined payroll tax rate could be increased during the >period in a manner equivalent to an immediate and permanent increase of >1.89 percentage points, benefits could be reduced during the period in >a manner equivalent to an immediate and permanent reduction of 12.6 >percent, general revenue transfers equivalent to $3.7 trillion (in >present value) could be made during the period, or some combination of >approaches could be adopted. Significantly larger changes would be >required to maintain solvency beyond 75 years. >http://www.ssa.gov/OACT/TR/TR04/II_highlights.html#wp76455 >T.Carr === Subject: Re: Question about President's Social Security plan >>by the amount of $2.7 trillion in 75 years. >>Bush administration has a plan. The plan is >>to privatize some parts of social security. >>This will cost $2 trillion to set up. >>It is not guaranteed to fix things, but >>is only one part of an integrated plan. >>So my question is, wouldn't it make more >>sense to just GIVE that $2 trillion to >>social security, which is guaranteed >>to fix things by exactly $2 trillion, just >>leaving a small $0.7 trillion shortfall after >>75 years? Of course that would make sense. But you have to understand that this will not help Bush and his rich friends and so it will not be supported by the Republicans. > You mean other then this train wreck if the media ever made this > information Public?! I think that the actuarial problems of the current system have been well publicized. But there will always be a few stupeeedos who actually think they have knowledge that is special. > I mean name me just ONE Democrat that would still > be left in office if the public found out that they had been lied to > and that the Social Security funds were being stolen by the Democrats > for the last 60+ years? (snicker) Your indictment of Johnson is correct, but most of this thievery has been by Repugnicans for the last 25 years. They are the big deficit creators, not the Dems. > Here are the REAL facts > Social Security.92s vaunted trust fund doesn.92t exist; taxes paid into > Social Security are merely being handed over as benefits to other > people. There are probably 10 people in this country that do not already KNOW this. You seem to be one of those who have only recently become aware of this fact. > On May 2nd, President Bush announced the formation of a presidential > commission to deal with the Social Security crisis. The last such > commission, in 1983, had as its chairman Alan Greenspan. It > recommended enormous increases in taxes, and Congress dutifully > complied. Yes. That would be the Republican Greenspan sucking up to the Republican Reagan. http://GreaterVoice.org/econ/glossary/The_Great_Ray_Gun_Rip_Off.php ACCELERATES THE SCHEDULE OF TAX HIKES IN SOCIAL SECURITY ORIGINALLY PASSED IN 1977. THE SCHEDULE IS TO BE COMPLETED BY 1990 INSTEAD OF THE YEAR 2030.** . >Government spokesmen immediately patted themselves on their > backs for having saved Social security. We are likely in for more of > the same. The new commission.92s name is the Commission to Strengthen > Social Security. That can only mean more taxes. Sure! We have a lying Republican in the White House and a compliant Greenspan at the Fed. What else would you expect accept some piece of crap that will send billions of dollars to the people who financed Georgie's campaign. > The Bush administration, though, should not be trying to save Social > Security. For decades americans have been deceived by this program, > believing that their Social Security taxes are pouring into a fund set > aside expressly for the purpose of old age insurance for the > support of the elderly. This is a colossal lie and it is nothing short > of scandalous. The truth is, the vaunted Social Security trust fund > does not exist. Never has, never will. And most people of even minimal intelligence realize this. > Haven.92t we been told for decades that the government scrupulously, > almost religiously, maintains the Social Security trust fund? For the > truth, we have to go back to 1935, shortly after the creation of > Social Security. A man named George P. Davis contested the program in > court, claiming that taxation to support it was unconstitutional, > trampled on states.92 rights, and imposed an unjust monetary burden on > firms in which he had invested. A federal court rejected his claims, > but he won a favorable ruling from the First Circuit Court of > Appeals in Boston. Had that Appeals Court decision remained in force, > the entire Social Security Act would have been voided at the outset. > As expected, however, the federal government.92s Commissioner of > Internal Revenue, Guy T. Helvering, immediately appealed the matter to > the Supreme Court. Lawyers for Mr. Davis contended that Social > Security taxes were collected for a particular purpose (for > unemployed and older Americans) and not for the constitutionally > acceptable purpose of acquiring revenue for the general welfare of the > nation as a whole. They also contended that the tax was not a > constitutionally allowable excise tax, a type of taxation defined > of use or consumption, not a tax on wages. > In Helvering v. Davis, the Supreme Court.92s decision made reference to > a related case wherein the court had tortuously maintained that the > tax was indeed an excise tax and therefore legitimate. But the Court > also agreed with the government.92s lawyers who had openly stated > that social security taxes were not collected for a particular purpose > but are paid into the Treasury as internal revenue collections, > available for the general support of the government. > That contention, forming the government.92s major argument against the > claims by Mr. Davis, received official endorsement when the Supreme > Court ruled in Helvering that the proceeds of the unemployment and > old-age taxes are to be paid into the Treasury like internal- > revenue taxes generally, and are not earmarked in any way. (Emphasis > added.) This decision has never been overturned. All talk about the > social security trust fund containing social security tax revenue is > pure, unadulterated blather. Yep. <<<<> > NOW do you see why the Democrats are so terrified about this SS > reform? They would be hanged and drawn'n'quartered if the seniors ever > found out that they were stealing from them. The government has been stealing from the working people of this country ever since the 1980 hike in FICA tax by the Reagan thieves. > The Democrats would never > be elected to dog warden ever again if this was made public, and part > of the reform is to MAKE THIS PUBLIC! You Democrats are staring down > the barrel of a loaded gun in your own hands, and for some reason your > pulling the trigger..... There is little most of us want more than to change the funding side of SS without touching the benefits side. -- I know no safe depository of the ultimate powers of society but the people themselves; and if we think them not enlightened enough to exercise their control with a wholesome discretion, the remedy is not to take it from them, but to inform their discretion by education. - Thomas Jefferson. http://GreaterVoice.org === Subject: Re: Question about President's Social Security plan >So my question is, wouldn't it make more >sense to just GIVE that $2 trillion to >social security, which is guaranteed >to fix things by exactly $2 trillion, just >leaving a small $0.7 trillion shortfall after >75 years? If we had dealt with the problem 20 years ago it would have cost a lot less to fix. Reagan tried but Congress refused to rein in entitlements. They simply raised the FICA and threw more money at it hoping that by the time anyone got wise they'd all be retired (on a FEDERAL pension) themselves. Clinton hemmed and hawed for 8 years and held blue ribbon commissions whose recommendations he quietly filed away for the next Administration to act on. Meanwhile the problem got bigger, not better. Setting aside a small fraction of the FICA taxes to allow workers to invest in their own pension plans doesn't actually cost Social Security anything. There is no lockbox full of money being set aside to pay retirees; it all comes out of the General Revenue fund anyway. These retirement accounts will generate enough taxable revenue to offset the loss in FICA taxes going into the system; they'll create new revenue streams into the Treasury. Put it like this. Right now you get ~ 1.75% annual return on your FICA investment, paid out of the Treasury when you retire. If you invested that money privately you'd get at least that and probably much more, paid out of the growth in the GDP between now and retirement. In effect it's a redistribution of wealth (which should make liberals happy but go figure) because what you don't tap from that revenue stream goes into the pockets of wealthy investors and multinational corporations. -- Iraq was a brilliant campaign fought with minimal casualties, 11 September was a humiliating failure by government to fulfill its primary role of national defence. But Democrats who complained that Bush was too slow to act on doubtful intelligence re 9/11 now profess to be horrified that he was too quick to act on doubtful intelligence re Iraq. This is not a serious party. === Subject: Re: Question about President's Social Security plan <57u6s0tmu6hrfdaqsjirlk290r7u5p3v4l@4ax.com> > Put it like this. Right now you get ~ 1.75% annual return on your > FICA investment, paid out of the Treasury when you retire. If you > invested that money privately you'd get at least that and probably > much more, paid out of the growth in the GDP between now and I figure it differently. If this applied to one or two individuals, it would indeed work the way you say. But when applied to entire populations, I think it would work another way. All this money is going to be put in one particular area of the economy - the stock market. The stock market operates on demand and supply. While the money is going in, the stock market goes up and absorbs all the money. Now recall that the whole problem is that at some point, there are going to be many more retirees than contributors to the system. Shifting it to the stock market is not going to change that fundamental characteristic. At some point, there simply will be many more sellers than buyers. When that happens, the stock market adjusts by going down. Given the volume of the movements, and the fact that the smart money will have flown out of the stock market a little earlier, it will crash. So the situation is, instead of the ~1.75% return there will be tremendous loss of capital. > retirement. In effect it's a redistribution of wealth (which should Yes, in effect it is indeed nothing but a redistribution of wealth. But I don't agree with the direction you seem to think it works in. === Subject: Re: Question about President's Social Security plan >> Put it like this. Right now you get ~ 1.75% annual return on your >> FICA investment, paid out of the Treasury when you retire. If you >> invested that money privately you'd get at least that and probably >> much more, paid out of the growth in the GDP between now and >I figure it differently. If this applied to one or two individuals, >it would indeed work the way you say. But when applied to entire >populations, I think it would work another way. >All this money is going to be put in one particular area of >the economy - the stock market. or the real estate market, or the municipal bond market, or any of a hundred other investments. Historically all of these have outperformed Social Security over time. Most pension plans don't put all their eggs in one basket, like Social Security does. SS is REQUIRED BY LAW to invest in the infusion of new workers over time and we know that ain't gonna happen; just the opposite is happening. -- Iraq was a brilliant campaign fought with minimal casualties, 11 September was a humiliating failure by government to fulfill its primary role of national defence. But Democrats who complained that Bush was too slow to act on doubtful intelligence re 9/11 now profess to be horrified that he was too quick to act on doubtful intelligence re Iraq. This is not a serious party. === Subject: Re: Question about President's Social Security plan <57u6s0tmu6hrfdaqsjirlk290r7u5p3v4l@4ax.com> >> Put it like this. Right now you get ~ 1.75% annual return on your >> FICA investment, paid out of the Treasury when you retire. If you >> invested that money privately you'd get at least that and probably >> much more, paid out of the growth in the GDP between now and >I figure it differently. If this applied to one or two individuals, >it would indeed work the way you say. But when applied to entire >populations, I think it would work another way. >All this money is going to be put in one particular area of >the economy - the stock market. > or the real estate market, or the municipal bond market, or any of a > hundred other investments. Historically all of these have > outperformed Social Security over time. Most pension plans don't put > all their eggs in one basket, like Social Security does. SS is > REQUIRED BY LAW to invest in the infusion of new workers over time and > we know that ain't gonna happen; just the opposite is happening. Think you missed the point here. What do you think is going to happen to interest rates when massive amounts of money are pulled out of the government bond market? No doubt this would have a big impact on the stock market as interest rates go way up which could result in a negative return for the stock market and a detrimental impact on the economy. And why do you assume that real estate is a safe investment? Have you ever heard of people making a bad investment? What will happen to those who invest in riskier investments and see their retirement fund wiped out? > -- > Iraq was a brilliant campaign fought with minimal > casualties, 11 September was a humiliating failure > by government to fulfill its primary role of > national defence. But Democrats who complained that > Bush was too slow to act on doubtful intelligence > re 9/11 now profess to be horrified that he was too > quick to act on doubtful intelligence re Iraq. This > is not a serious party. I am amazed that a president who outright lied over the reason to go to war in Iraq, WMD that did not exist was reelected. Iraq and 9/11 are unrelated events or at least thats the conclusion of the 9/11 commission === Subject: Re: Question about President's Social Security plan >by the amount of $2.7 trillion in 75 years. >Bush administration has a plan. The plan is >to privatize some parts of social security. Bush has a notion, not a plan. The actual plan, following the precedent of Cheney's energy plan, will be prepared by brokerages and mutual funds, with their recommendations being weighted according to their contributions to the GOP. === Subject: Re: Question about President's Social Security plan >by the amount of $2.7 trillion in 75 years. >Bush administration has a plan. The plan is >to privatize some parts of social security. > Bush has a notion, not a plan. > The actual plan, following the precedent of Cheney's energy plan, > will be prepared by brokerages and mutual funds, with their > recommendations being weighted according to their contributions to > the GOP. Bush does have something in it for him, too. It will leave the stock market jumping for joy, and Bush's legacy will be to leave the economy booming. Whether it's a false or temporary boom, won't be his concern. And in any case, he will have lots of defenders who will claim the followup bubble-bursting and social-security money getting swallowed up by the smart crowd, was caused by the evil lefties and had nothing to do with the original mighty grand plan... === Subject: Re: Question about President's Social Security plan This [privatize some parts of social security] will cost $2 trillion to set up. So my question is, wouldn't it make more sense to just GIVE that $2 trillion to social security, which is guaranteed to fix things by exactly $2 trillion, just leaving a small $0.7 trillion shortfall after 75 years? The counter-argument would be that in doing so you'd simply be perpetuating a poor system that by your own words remains in deficit, still will be unsustainable because of its design, and you are also erroneous (if not deliberately misleading) by referring to $0.7 trillion as small. There are other counter-arguments as well (you fail to view the entire exchange of revenues and benefits, for example). You were on stronger ground elsewhere on this thread when you rightly noted that Wall Street would love to get its hands and and make money off all that money. Government would indirectly be giving money (taxing it and seeing that it was redirected) to Wall Street. A more legitimate problem with Bush's proposal is this would be nominally private but still would be a government-program set of accounts, and there would be temptations by Democrats, especially liberal Democrats, to engage in evil, anti-American lefty-fascist follies that Ralph Nader only could dream of decades ago, such as making the federal government the largest-by-far institutional investor -- and with that would come government influence and social responsibility, faddish far-left idiocy such as Israeli divestiture gimmicks, maybe government shareholder influence on politically disfavored industries like guns and automobiles, and so on. No normal American wants any threat of that. === Subject: Re: Question about President's Social Security plan > A more legitimate problem with Bush's proposal > is this would be nominally private but still would be > a government-program set of accounts, and there > would be temptations by Democrats, especially > liberal Democrats, to engage in evil, anti-American > lefty-fascist follies that Ralph Nader only could > dream of decades ago, such as making the > federal government the largest-by-far institutional > investor -- and with that would come government > influence and social responsibility, faddish far-left > idiocy such as Israeli divestiture gimmicks, maybe > government shareholder influence on politically > disfavored industries like guns and automobiles, and > so on. No normal American wants any threat of that. I can't imagine that political agitation for restriction of these investments would be confined to the left. Would the backers of this plan permit any of the money to be invested in ,for instance, manufacturers of contraceptives, particularly the so-called morning after pill? I have a plan that would make SS solvent for the rest of this century. Just increase the interest rate that the general fund pays to the Social Security fund by one percentage point. The same amount of cash that changes hands would be the same as present, but the SS fund has immediately become much more solvent due to the increase in the future value of its reserves. Just bookkeeping, but that is all claims of SS insolvency are anyway. -- To e-mail me get rid of the cats and dogs. === Subject: Re: Question about President's Social Security plan >> A more legitimate problem with Bush's proposal >> is this would be nominally private but still would be >> a government-program set of accounts, and there >> would be temptations by Democrats, especially >> liberal Democrats, to engage in evil, anti-American >> lefty-fascist follies that Ralph Nader only could >> dream of decades ago, such as making the >> federal government the largest-by-far institutional >> investor -- and with that would come government >> influence and social responsibility, faddish far-left >> idiocy such as Israeli divestiture gimmicks, maybe >> government shareholder influence on politically >> disfavored industries like guns and automobiles, and >> so on. No normal American wants any threat of that. > I can't imagine that political agitation for restriction of these >investments would be confined to the left. >Would the backers of this plan permit any of the money to be invested >in ,for instance, manufacturers of contraceptives, particularly the >so-called morning after pill? >I have a plan that would make SS solvent for the rest of this century. >Just increase the interest rate that the general fund pays to the Social >Security fund by one percentage point. The same amount of cash that >changes hands would be the same as present, but the SS fund has >immediately become much more solvent due to the increase in the future >value of its reserves. The SS tax was dramatically increased under Reagan and he used the money to fund the tax breaks for the wealthy and his monstrous increase in military spending to go to war against Russia and the Middle East (Iraq and Iran). Charlie >Just bookkeeping, but that is all claims of SS insolvency are anyway. >-- >To e-mail me get rid of the cats and dogs. === Subject: Re: Question about President's Social Security plan > The counter-argument would be that in doing so > you'd simply be perpetuating a poor system that > by your own words remains in deficit, still will be > unsustainable because of its design, and you are I thought the problem was not the design, but baby boomers. Reverse booms should put money into social security, which could then be used up for the next boom. > also erroneous (if not deliberately misleading) by > referring to $0.7 trillion as small. Not looked at the budget figures lately, have we? Maybe you have a point -- perhaps it's erroneous in this context to call 0.7 trillion over 75 years as small. It's better called negligible or trivial or irrelevant. Any single one of the next presidents over the next 75 years could fix it when the need became apparent. In the worse case, by borrowing (just like Bush plans to do), in the best case by using up some surplus. === Subject: Re: Question about President's Social Security plan > I thought the problem was not the design, but > baby boomers. Reverse booms should put money > into social security, which could then be > used up for the next boom. Reverse booms??? The problem is both with the design and with demographics (not merely the Baby Boomers but lower fertility rates and longer lifespans). The program, if kept (which is most likely), should be converted to fully funded rather than as pay-as-you go. Also, it is irresponsible (and given our lives are involved, illogical) to count on recovery of the program after the Baby Boomers are dead, much less to be superficial in our approach and simply tax more during low-beneficiary-number years or decades to better finance benefits during high-beneficiary-number years or decades that follow them. > Not looked at the budget figures lately, have we? I'm fully aware of them, as well as what Social Security and Medicare will do to the entire federal budget (not just those two programs) long before either of these two programs go bankrupt. > Maybe you have a point -- perhaps it's erroneous > in this context to call 0.7 trillion over 75 years > as small. It's better called negligible or trivial > or irrelevant. That's even more erroneous. > Any single one of the next presidents over the next > 75 years could fix it when the need became > apparent. In the worse case, by borrowing (just like Bush > plans to do), in the best case by using up some surplus. Only a fool would count on a surplus then, much later, the realistic time when politicians will take action -- which is only when forced to, or in other words -- eventually. (They avoid doing anything unpleasant now even though it solves worse problems for us later.) There will not be an easy fix later. Note that you say that at any time, it can be fixed. That is the admission of error of all those who deny there is anything wrong with the system now. (There is; it is unsustainable and will cause many other fiscal problems for the federal government long before it goes broke.) If it were up to me and we had to keep Social Security, I would take the roughly ten years we have left before the Baby Boomers start their retirements to convert from our pay-as-you-go (Ponzi scheme) system to a fully funded system. As that causes some pain to all, perhaps it is that one time conversion that might, might justify borrowing, because it would solve the problem with not only S.S. but with the federal finances, and so justify the extra cost of interest in the long run. === Subject: Re: Question about President's Social Security plan > Maybe you have a point -- perhaps it's erroneous > in this context to call 0.7 trillion over 75 years > as small. It's better called negligible or trivial > or irrelevant. > That's even more erroneous. I think I was not clear enough. I will simplify. It works out to less than 10 billion per year. How big a deal in the federal budget do you want to make that? > There will not be an easy fix later. Sure there will be. Note that Bush's fix involves borrowing $2 trillion. What's to stop a future president, who is facing the problem here and now instead of in the future, to simply borrow the much smaller amounts needed to keep it solvent, as and when needed? And it is indeed possible that when needed, the budget will happen to have a surplus, at least some of the times. === Subject: Re: Question about President's Social Security plan > by the amount of $2.7 trillion in 75 years. > Bush administration has a plan. The plan is > to privatize some parts of social security. > This will cost $2 trillion to set up. > It is not guaranteed to fix things, but > is only one part of an integrated plan. > So my question is, wouldn't it make more > sense to just GIVE that $2 trillion to > social security, which is guaranteed > to fix things by exactly $2 trillion, just > leaving a small $0.7 trillion shortfall after > 75 years? Your solution makes too much sense. Forget about it in this administration. === Subject: Re: Question about President's Social Security plan John Deere says... >by the amount of $2.7 trillion in 75 years. >Bush administration has a plan. The plan is >to privatize some parts of social security. >This will cost $2 trillion to set up. >It is not guaranteed to fix things, but >is only one part of an integrated plan. >So my question is, wouldn't it make more >sense to just GIVE that $2 trillion to >social security, which is guaranteed >to fix things by exactly $2 trillion, just >leaving a small $0.7 trillion shortfall after >75 years? You're assuming that Bush *wants* to fix social security. Nothing could be farther from the truth. He wants to make sure that it goes bankrupt, and his privatization plan is a crucial step. -- Daryl McCullough Ithaca, NY === Subject: Re: Question about President's Social Security plan > You're assuming that Bush *wants* to fix social security. > Nothing could be farther from the truth. He wants to make > sure that it goes bankrupt, and his privatization plan is > a crucial step. I've seldom seen anyone mention what I think is the real reason for the Bushist Social Security plan. As social security money moves from the Trust Fund (U.S. Treasury bonds) to private accounts (stocks), there will be a strong upward pressure on U.S. stock prices. This will be a windfall for those who already own stocks -- i.e. Bush's constituency -- though those the program supposedly helps will be buying stocks at inflated prices. Every dollar diverted to the private accounts, whether subtracted from the Trust Fund or from current retirement payouts, will represent a dollar of increased (non Trust Fund) Treasury borrowing, so interest rates will almost certainly rise and the supposed reason for the plan (stocks outperform bonds) will prove tragically false. (Even after the 2000 crash, stocks are always a good long-term investment is prattled as a law of nature, with NYSE history cited as proof. Try the same long-term historic study with German stocks!) James Dow Allen === Subject: Re: Question about President's Social Security plan > ...stocks are always a good > long-term investment is prattled as a law of nature, > with NYSE history cited as proof. Try the same long-term > historic study with German stocks!) Someone will rebut by saying U.S.A. has a strong efficient economy, while 20th century Germany made big mistakes. Put the first clause in the past tense please, and note that U.S.A. is making big mistakes right now. James === Subject: Re: Question about President's Social Security plan > You're assuming that Bush *wants* to fix social security. > Nothing could be farther from the truth. He wants to make > sure that it goes bankrupt, and his privatization plan is > a crucial step. I don't think he particularly cares to see social security bankrupt -- I suspect the motivation is entirely different. Wall Street was helped strongly during the internet bubble by 401K funding. The major players made tons of money. But then the bubble burst, and the wall street honchos felt they weren't rich enough. They saw a ray of light -- the next possible bubble could come from social security. So they are pulling all kinds of strings. And of course, our venerable president is a sucker for anything the rich guys say -- it must be the right thing to do if the havemores say so. He just doesn't believe the nice havemores would advise something that could have bad results. It's kind of Darwinian. Remeber, the folks who would be most exploited are mostly staunch Bush supporters, and would jump at anybody with both feet for suggesting he is doing something wrong. I don't know how much is really wrong if they are left -- by the actions of their favorite president -- with nothing in their golden days. Besides, they will blame the lib dem boogiemen anyways. And I suppose if it does go through, the smart folks could make some money at the expense of these non-havemore Bush supporters, because the stock market will have some irrational moments. Still, it just doesn't seem right, or American, or a good thing at all for the long term future. === Subject: Re: Question about President's Social Security plan >by the amount of $2.7 trillion in 75 years. >Bush administration has a plan. The plan is >to privatize some parts of social security. >This will cost $2 trillion to set up. >It is not guaranteed to fix things, but >is only one part of an integrated plan. >So my question is, wouldn't it make more >sense to just GIVE that $2 trillion to >social security, which is guaranteed >to fix things by exactly $2 trillion, just >leaving a small $0.7 trillion shortfall after >75 years? Yes, except that the government doesn't have an account with $2 trillion in it. So it would have to sell bonds in that amount. The simpler method is to directly credit the SS trust fund with whatever it needs to cover the shortfall, if and when it occurs. === Subject: Re: Question about President's Social Security plan >Yes, except that the government doesn't have an account with $2 >trillion in it. So it would have to sell bonds in that amount. The >simpler method is to directly credit the SS trust fund with whatever >it needs to cover the shortfall, if and when it occurs. Except of course the government would have to print money to cover the shortfall which would quickly lead to hyperinflation. You can issue bonds but there has to be some expectation that you can pay off those bonds when they come due, you see, and with 95% or whatever percent of the federal budget dedicated to paying pension checks that doesn't leave much room to pay any other bills. Ideally you take care of this by increasing the contributions slightly well in advance and restraining the growth of the program to inflation. If we had done this back in, oh, 1983 the system would be solvent. Unfortunately we only did *half* of this: We raised FICA taxes and declared we had a surplus. But Congress never reined in entitlements and then spent the FICA surplus on other things. Bottom line is the surplus disappears from the books around 2011 and from that point on the system runs in the red. And it only gets *redder* the further out you go, with too few workers paying into the system to cover benefits going out. -- Iraq was a brilliant campaign fought with minimal casualties, 11 September was a humiliating failure by government to fulfill its primary role of national defence. But Democrats who complained that Bush was too slow to act on doubtful intelligence re 9/11 now profess to be horrified that he was too quick to act on doubtful intelligence re Iraq. This is not a serious party. === Subject: Re: Question about President's Social Security plan OrionCA says... >Iraq was a brilliant campaign fought with minimal >casualties, 11 September was a humiliating failure >by government to fulfill its primary role of >national defence. But Democrats who complained that >Bush was too slow to act on doubtful intelligence >re 9/11 now profess to be horrified that he was too >quick to act on doubtful intelligence re Iraq. This >is not a serious party. Whoever said that is not a serious commentator. The comparison is stupid. -- Daryl McCullough Ithaca, NY === Subject: Re: Question about President's Social Security plan >OrionCA says... >>Iraq was a brilliant campaign fought with minimal >>casualties, 11 September was a humiliating failure >>by government to fulfill its primary role of >>national defence. But Democrats who complained that >>Bush was too slow to act on doubtful intelligence >>re 9/11 now profess to be horrified that he was too >>quick to act on doubtful intelligence re Iraq. This >>is not a serious party. >Whoever said that is not a serious commentator. The >comparison is stupid. Brilliant counterargument there. Mark Stein, btw, is a respected political commentator both in the UK and the United States. And he was absolutely correct in his statement. you are not a serious political party anymore. -- Iraq was a brilliant campaign fought with minimal casualties, 11 September was a humiliating failure by government to fulfill its primary role of national defence. But Democrats who complained that Bush was too slow to act on doubtful intelligence re 9/11 now profess to be horrified that he was too quick to act on doubtful intelligence re Iraq. This is not a serious party. === Subject: Re: Question about President's Social Security plan >>Yes, except that the government doesn't have an account with $2 >>trillion in it. So it would have to sell bonds in that amount. The >>simpler method is to directly credit the SS trust fund with whatever >>it needs to cover the shortfall, if and when it occurs. >Except of course the government would have to print money to cover the >shortfall which would quickly lead to hyperinflation. The government prints money, i.e. monetizes the debt, for only two reasons: (1) to meet the public's demand for wallet money in lieu of bank deposits, and (2) to provide the reserves banks need to meet their reserve ratio requirements. Future payments to social security beneficiaries will not require the printing of money. It will involve deficit spending, all of which will be covered by the sale of bonds. >You can issue >bonds but there has to be some expectation that you can pay off those >bonds when they come due, you see, and with 95% or whatever percent of >the federal budget dedicated to paying pension checks that doesn't >leave much room to pay any other bills. The Treasury has no problem redeeming its bonds, and never will. The amount of government spending going to social security and medicare is currently about 35% of the total spending. That will increase as baby boomers retire, but it will never come close to 95% of total spending. >Ideally you take care of this by increasing the contributions slightly >well in advance and restraining the growth of the program to >inflation. If we had done this back in, oh, 1983 the system would be >solvent. The program is solvent and will be for at least forty years. If and when the trust fund runs out, the shortage can be made up by government borrowing. That will increase the deficit, but only during the peak years of benefits for baby boomers. They too will die. >Unfortunately we only did *half* of this: We raised FICA >taxes and declared we had a surplus. But Congress never reined in >entitlements and then spent the FICA surplus on other things. There is no way the FICA surplus can be kept in a lock box. Those funds would be spent even if the on-budget were in balance. >Bottom line is the surplus disappears from the books around 2011 and >from that point on the system runs in the red. And it only gets >*redder* the further out you go, with too few workers paying into the >system to cover benefits going out. The surplus FICA revenues are expected to disappear about 2018, which simply means the so-called trust fund will stop increasing in value at that time. It is conservatively projected to remain in the black decades longer. === Subject: Re: Question about President's Social Security plan : by the amount of $2.7 trillion in 75 years. : : Bush administration has a plan. The plan is : to privatize some parts of social security. : : This will cost $2 trillion to set up. : : It is not guaranteed to fix things, but : is only one part of an integrated plan. : : So my question is, wouldn't it make more : sense to just GIVE that $2 trillion to : social security, which is guaranteed : to fix things by exactly $2 trillion, just : leaving a small $0.7 trillion shortfall after : 75 years? : Why not just level with the people and tell them Social Security is an unconstitutional use of their money and in 25 years that will cease? So, all you nice folks that have been letting the government have some walking around cash better start saving now for that rainy day coming up 25 years from now. -- Who are these guys? If the world were a logical place, men would ride horses sidesaddle Smith or Jones === Subject: Re: Question about President's Social Security plan > Why not just level with the people and tell them Social Security is an > unconstitutional use of their money and in 25 years that will > cease? There's nothing unconstitutional about social security. Paul Krugman on Social Security, the Decline of the Dollar and Healthcare ------------------------------------------------------------------------ New York Times columnist and Princeton economics professor, Paul Krugman discusses President Bush's Social Security plan, the devaluation of the dollar and the healthcare debate. [includes rush transcript] ------------------------------------------------------------------------ The Bush press conference yesterday wasn't only on international issues. Several reporters questioned the president on what many see as one of the premiere domestic issues now facing the country: social security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking out an explicit, principled position in favor of dodging the question. Here is one of the exchanges Bush had with reporters when asked about his social security plan. That was President Bush, well, not answering a question on Social Security. We are joined now by New York Times columnist Paul Krugman. He has been writing a lot on this issue. One of his latest columns is called Buying into Failure, where he accuses the Bush administration of trying to convert Social Security into a giant 401(k). *Paul Krugman, New York Times columnist and Professor of Economics at Princeton University. His latest book The Great Unraveling: Losing Our Way In The New Century is a collection of his New York Times columns. Bush's news conference yesterday, the Bush news conference wasn't only on international issues. Several reporters questioned the president on what many see as one of the premier domestic issues now facing the country. Social Security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking a principled position while dodging the question. Here is one of the exchanges Bush had with reporters when asked about the Social Security plan. reform the top of your domestic agenda for a second term. You have been talking extensively about the benefits of private accounts, but by most estimations, private accounts may leave something for young workers at the end, but wouldn't do much to solve the overall financial problem with social security. I'm just wondering, as you promote the private accounts, why aren't you talking about the tough measures that need to be taken to preserve Social Security such as increase the retirement age, cutting benefits or means testing for Social Security? GEORGE W. BUSH: I appreciate the question. Let me put the Social Security issue in proper perspective. It is a very important issue, but it's not the only issue - very important issue, we'll be dealing with. I expect the Congress to bring forth meaningful tort reform. I want the legal system reformed in a way that we can -- we are competitive in the world. I will be talking about the budget, of course. There's a lot of concern in the financial markets about our deficits, short-term and long-term deficits. The long-term deficit is caused by some of the entitlement programs, the unfunded liabilities inherent in the entitlement programs. I will push on an education agenda. No doubt in my mind that the No Child Left Behind Act is meaningful, a real reform having real results. And I look forward to strengthening No Child Left Behind. Immigration reform is also very important agenda item as we move forward. But Social Security, as well, is a big item. I campaigned on it, as you are painfully aware, since you had to suffer through many of my speeches. I didn't duck the issue like others have done in the past. I said this is a vital issue, and we need to work together to solve it. Now, the temptation is going to be, by well-meaning people such as yourself, John, and others here as we run up to the issue, to get me to negotiate with myself in public to say, you know, what's this mean, Mr. President? What's that mean? I'm not going to do that. I don't get to write the law. I'll propose a solution at the appropriate time, but the law will be written in the halls of Congress. I will negotiate with them, with the members of Congress, and they will want me to start playing my hand. Will you accept this, will you not accept that, why don't you do this hard thing, why don't you do that. I recognize, this is going to be a decision that requires difficult choices, John. Inherent in your question I do recognize that, you bet I do. Otherwise, it would have been done. So, I am just -- I just want to condition you. I'm not doing a very good job, because the other day in the Oval Office, when the press pool came in, I was asked about this -- the series of questions -- a question on Social Security with these different aspects to it. And I said, I'm not going to negotiate with myself. I will negotiate at the appropriate time with the law writers. So, thank you for trying. The principles I laid out in the course of the campaign and the principles we laid out in the recent economic summit are still the principles I believe in. That is, nothing will change for those near our Social Security payroll. You were the one that asked me whether the payroll tax, if I'm not mistaken, will not go up. And I know there's the big definition about what that means. Well, again, I will repeat -- don't bother to ask me. Or, you can ask me. I can't tell you what to ask. That's not the holiday spirit. But I'm -- it is all part of trying to get me to set the parameters -- you know, apart from the Congress, which is not a good way to get substantive reform done. Krugman joins us on the line now, columnist for The New York Times, professor of economics at Princeton University, his latest book, The Great Unraveling: Losing Our Way in the New Century, a collection of his Times pieces. Welcome to Democracy Now! PAUL KRUGMAN: Good morning. PAUL KRUGMAN: This is a -- this is a unique excuse. I mean, I got to give him some credit. He says, Mr. President, your stuff doesn't add up. You're saying that two minus one equals four. What are you going to throw in? He says, don't get me to try to negotiate with myself. This is new. The important thing to say here is that Social Security is way down on the list of problems we have got. If you were going to take a look at just the budget, we have a huge, immediate problem on the deficit about which Bush intends to do nothing, really. We have a very serious problem on Medicare and Medicaid, which is a big issue. Social Security is the bright spot. It has maybe some mild financial problems, several decades out, and here we are -- he wants a crisis there, partly to distract from the very real crises in other places, and there you go. Because it's not just President Bush. If he was raising questions about it with a little megaphone on the steps of the White House, it would not have the kind of effect it was having without all of the media, it seems, amplifying the idea that Social Security is broken. It's bankrupt. PAUL KRUGMAN: Right. And of course, that's really a question about the media, not about Social Security. Social Security is a program which has been traditionally run. It looks like a retirement fund, and it is not exactly. What it really is is a government program with a dedicated tax. We take the payroll tax and it's used to pay benefits to retirees. And 20-plus years ago, the commission led by Alan Greenspan said, you know, we are going to have this problem as the baby boomers reach retirement age. We will have a higher ratio of retirees to workers, and we better get ready for it. Social Security, the payroll tax was increased. There were some other things, a small rise in the retirement age set in motion. So that Social Security would run a surplus, which would be used to accumulate a trust fund, and this would tithe us over, some ways into the aging of the population. And that on its own accounting is working just fine. I mean, one of the things that we need to know is that the estimates of the day at which the trust fund runs out, just keep on receding further into the future, because the program is doing so well at running surpluses. So, ten years ago, people said it was going to run out in 2029. Now the official estimate is 2042. Realistically, it's probably going to go well into the second half of the century. Now how does this become a crisis? Well it becomes a crisis by changing the rules. By saying, oh, well, actually, that surplus that we're running because of the tax increase that was designed to prolong the life of Social Security, that's not real. Because it's invested in government bonds which are a perfectly good asset, for anybody else, but not for the Social Security administration. And so, there was a real crisis that people saw in the 1980's. They dealt with it. The solution worked very well, but because this administration, because the Republican party doesn't want Social Security to remain, because they have always wanted to get rid of it since Franklin Roosevelt, they have decided to redefine the rules so as to call it a crisis when realistically, we have a huge budget problem, but that has nothing to do with Social Security. take a break. We're talking to New York Times columnist, Princeton University professor, Paul Krugman. [break] York Times. He teaches at Princeton University. His latest book, The Great Unraveling. We're talking about Social Security and other issues raised by President Bush in his 17th news conference yesterday. You talked about the real problem with the budget. I want to get to that in a minute, but what about the issue of, you said, this is really a problem with how Social Security is being conveyed, not so much with President Bush as with the media? PAUL KRUGMAN: Yeah. This is an issue where at the very least there are -- there's great dissension among people who have -- there is by no means a consensus among people who actually know something about the subject that there is a Social Security problem and certainly no consensus, there is a crisis. This is a front burner issue. But if you got your news from TV or, to a large extent, even the newspapers, you would never know that. The reporting has simply bought into the White House spin, and people who offer a different point of view are simply not considered, you know, just not part of the discussion. It's kind of like a -- well it's like the threat from Iraq, to take a random analogy. PAUL KRUGMAN: I think the thing to do is to -- I mean, certainly what I will be doing once I'm back full time at the Times is keep on hammering what the realities are and also on the fact that other countries have actually gone down the road that the Bush administration wants us to go down and the results have not been happy. So, to just say, look, this is where -- this is a phony solution to a phony crisis, and hope that at least we can get some traction. But I have to say it's pretty frustrating. You cannot get the alternative view -- which happens to be the majority of view that people who have actually studied the subject -- just can't get it on the air. its impact? PAUL KRUGMAN: Not sure what it has to do with Social Security, but we are having a -- look, the United States is running huge twin deficits. The federal government is borrowing $1 billion a day or so for the operations. The United States as a whole is borrowing $1.5 billion to pay for imports. Those can't go on forever. It's a law that says that things that cannot go on forever don't, and it appears that the world is finally looking at it and saying, Gee, we don't see this changing, and so, the money flows are starting to dry up. The dollar is falling. We don't know how it plays out. If this was a Third World country, and you had the numbers we have, you would say, Oh, my God, start stocking up on canned goods, because we look by many of the numbers worse than places like Argentina or Indonesia. But it is the United States. We get a lot of the benefit of the doubt. The debts are in dollars, which is some protection, having the debts in our own currency. But it's going to be -- it just adds to the difficulties. where do you see the crisis in the budget really is? PAUL KRUGMAN: Well, if you look at why are we -- why have we gone from surpluses to deficits? The answer is about one-quarter, roughly -- roughly, one-quarter of it is extra defense spending. Three-quarters is a plunge in revenues. And the plunge in revenues is -- a large part of it is directly the result of the Bush tax cuts. A lot of the rest we don't quite understand. It's capital gains that were a big thing in the late 1990s that dried up. Probably an increase in tax evasion and avoidance because of the political climate is favorable to that. We don't really know. But the point is, what's really happening is we're just not bringing enough tax revenue to pay for the operations of government right now and it's -- but that's off the table. Doing something to enhance revenue is clearly, from the point of view of this White House and this current ruling party, something you just don't do. And there is really no way that I can see that the spending is going to be cut enough. So, we have a deficit, which is -- which our political system is now unwilling to be realistic, unwilling to contemplate doing what has to be done to bring it down significantly. tax cuts to be made permanent. Your response to that? PAUL KRUGMAN: Well, then the question is what -- is he prepared to be honest and say that And we're going to slash Medicare benefits, slash Social Security benefits, not for people 30 years from now but people in the near term? Because you can't run deficits this size indefinitely, and you can't cut these deficits significantly without either raising taxes or making big cuts where the money is, and this -- the federal government is basically -- as number of people have said, it's basically a big insurance company with a side business in national defense. Aside from Medicare, Medicaid, Social Security and national defense, there just isn't much there. So the only way you can really pay for bringing the deficit down significantly is with big cuts in the programs that people have come to count on in their lives. occupation of Iraq on the budget in this country? PAUL KRUGMAN: Well, it's a -- I mean, roughly speaking, it's about a third of a Vietnam. That is, you are looking at - although it may be getting up to half of Vietnam, given some of the later cost estimates. It's a big expense. It's dwarfed in importance as a source of lost revenue by the tax cuts. Roughly speaking, the tax cuts are -- this past fiscal year, the tax cuts were responsible for about $270 billion of lost revenue, and the cost of the Iraq war probably was $70 billion or $80 billion. It's a little bit hard to figure out. It's a big thing, just adds to the fire, adds to the problems, but you know, I know people on -- liberals, particularly people who are horrified by the war would like to make it the root of all evil, but the truth is that on the fiscal side, it's a secondary source, compared with big tax cuts for people with very high incomes. Security -- exactly who profits right now from this debate? PAUL KRUGMAN: Well, that's -- we don't -- you know, since we don't have specifics, we don't know. I mean, what the Social Security privatization would do probably in the first place is it would probably end up removing a lot of the security features in Social Security. So that people -- you know, as it stands now, Social Security is much more than just a retirement program. It's a disability program. The way the benefits are structured tends to protect people against poverty. So, people -- the worst off would tend to be hurt and people who would have been fine without Social Security will do better, probably, as a result. Then the big question is, if we get these private accounts, how are they going to be handled? They are now saying, Oh, well, we'll put them in index funds which will generate almost no business, but now we hearing that will be for starters and then they'll relax the rules. There will be enormous lobbying pressure to relax the rules so that Wall Street gets a piece of the action, so it generates commissions. It privatized systems, they generate large commissions for the investment industry. They typically -- the operating costs are typically around 20 times as high as the operating costs of Social Security. And those are -- that all represents business for Wall Street. that we could look to as examples, that have gone through privatization? PAUL KRUGMAN: The stories -- the country that people like to point to is Chile. But what we're told is a myth about Chile. They privatized their retirement system, and lived happily ever after. The reality is that the returns on accounts of not been very good. Considering the -- you know, the fees have absorbed a large part, about probably 20% of the money put in. The other thing is that the system doesn't do the job of protecting people against poverty. Now, the good news for Chile is that from the beginning, they had a clause in there that said that the government steps in and supplements pensions if people don't have enough income to live on, basically, and that's what happens. The government ends up paying a lot of support. So, instead -- it isn't really -- they privatized it in part but it turned into a big expensive poverty support program in addition. So it just isn't doing the things that people claim it did. Britain has had a system of private pensions, and it's reaching the -- there was a big commission study, the Pensions Commission in Britain released a study in October saying that we're going to have a lot of poor older people that basically poverty among the elderly, which, in Britain as in the United States, had been greatly reduced by social insurance programs, is staging a comeback, and we're going to need to do a lot to help them out. So, these -- again, the fees to investment companies eat up a lot of the returns. So, you know, these systems are not -- they don't have the virtues that people claim for them and they actually turn out to do a lousy job of providing for people's retirement. touted as a success and it isn't. What about looking north to Canada? This is on the issue of health insurance, but how often in the media it is talked about as a complete failure, and what do you think of that? PAUL KRUGMAN: Well, the Canadians don't think so. Their health system is very popular. What is true is that the very best medical care in the U.S. is the best in the world. If you have a very good insurance program, if you are covered through your company in a way that's generous, then, the U.S. probably has somewhat better health care for you than you would get in Canada, although I actually probably don't want to say this, but the system that seems to be terrific on all dimensions is France. But anyway, the Canadian system at the very highest end is maybe slightly worse than ours. But large numbers of Americans don't get the best we can offer. In fact, the health insurance is -- the system of company-provided health insurance is cracking. The number of people in it is steadily declining. And so, we actually don't get very good coverage for many Americans. And that shows in really lousy health returns. The other thing, it's incredibly expensive. There's the myth about the efficiency of the private sector, which is true in some things, but it isn't when it comes to health insurance. In fact, the U.S. system is about twice as expensive per person as anyone else's, and we get worse results because we have basically insurance companies spending a lot of money, going to great efforts, in an effort not to cover people. All of which is wasted effort from the view of society. When you have a single-payer system, like in Canada, that doesn't happen. France, if you would dare to take it on. PAUL KRUGMAN: Just so to say that the French have a single-payer health care system. A lot of the details are different, but basically it's national health insurance. The difference between them and most other advanced countries is they actually fund it better. I mean, they -- the complaints that people have about -- the British system is the one that people say provides poor care, and apparently it largely does because the British don't spend enough money on it. The French do spend enough money on national health care and it's excellent. Infant mortality is much higher in the U.S. than it is in other advanced countries. Life expectancy is lower than it is in other advanced countries. And here we are claiming, saying, Yes, we have the best system in the world and look at how bad those other guys are. Let me tell you, when it comes to life and death, we don't do very well. us. Do you think that President Bush understands this to the point where -- this is why he vilifies France? PAUL KRUGMAN: I don't think so -- I think they have no idea. No. I doubt it. I think they -- he just has the -- I think our leadership is very insular. They just believe everything American must be best because they don't know what goes on elsewhere. Way in the New Century, columnist for The New York Times and Princeton University economist, joining us. === Subject: Re: Question about President's Social Security plan > Why not just level with the people and tell them Social Security is an > unconstitutional use of their money and in 25 years that will > cease? There's nothing unconstitutional about social security. Paul Krugman on Social Security, the Decline of the Dollar and Healthcare ------------------------------------------------------------------------ New York Times columnist and Princeton economics professor, Paul Krugman discusses President Bush's Social Security plan, the devaluation of the dollar and the healthcare debate. [includes rush transcript] ------------------------------------------------------------------------ The Bush press conference yesterday wasn't only on international issues. Several reporters questioned the president on what many see as one of the premiere domestic issues now facing the country: social security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking out an explicit, principled position in favor of dodging the question. Here is one of the exchanges Bush had with reporters when asked about his social security plan. That was President Bush, well, not answering a question on Social Security. We are joined now by New York Times columnist Paul Krugman. He has been writing a lot on this issue. One of his latest columns is called Buying into Failure, where he accuses the Bush administration of trying to convert Social Security into a giant 401(k). *Paul Krugman, New York Times columnist and Professor of Economics at Princeton University. His latest book The Great Unraveling: Losing Our Way In The New Century is a collection of his New York Times columns. Bush's news conference yesterday, the Bush news conference wasn't only on international issues. Several reporters questioned the president on what many see as one of the premier domestic issues now facing the country. Social Security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking a principled position while dodging the question. Here is one of the exchanges Bush had with reporters when asked about the Social Security plan. reform the top of your domestic agenda for a second term. You have been talking extensively about the benefits of private accounts, but by most estimations, private accounts may leave something for young workers at the end, but wouldn't do much to solve the overall financial problem with social security. I'm just wondering, as you promote the private accounts, why aren't you talking about the tough measures that need to be taken to preserve Social Security such as increase the retirement age, cutting benefits or means testing for Social Security? GEORGE W. BUSH: I appreciate the question. Let me put the Social Security issue in proper perspective. It is a very important issue, but it's not the only issue - very important issue, we'll be dealing with. I expect the Congress to bring forth meaningful tort reform. I want the legal system reformed in a way that we can -- we are competitive in the world. I will be talking about the budget, of course. There's a lot of concern in the financial markets about our deficits, short-term and long-term deficits. The long-term deficit is caused by some of the entitlement programs, the unfunded liabilities inherent in the entitlement programs. I will push on an education agenda. No doubt in my mind that the No Child Left Behind Act is meaningful, a real reform having real results. And I look forward to strengthening No Child Left Behind. Immigration reform is also very important agenda item as we move forward. But Social Security, as well, is a big item. I campaigned on it, as you are painfully aware, since you had to suffer through many of my speeches. I didn't duck the issue like others have done in the past. I said this is a vital issue, and we need to work together to solve it. Now, the temptation is going to be, by well-meaning people such as yourself, John, and others here as we run up to the issue, to get me to negotiate with myself in public to say, you know, what's this mean, Mr. President? What's that mean? I'm not going to do that. I don't get to write the law. I'll propose a solution at the appropriate time, but the law will be written in the halls of Congress. I will negotiate with them, with the members of Congress, and they will want me to start playing my hand. Will you accept this, will you not accept that, why don't you do this hard thing, why don't you do that. I recognize, this is going to be a decision that requires difficult choices, John. Inherent in your question I do recognize that, you bet I do. Otherwise, it would have been done. So, I am just -- I just want to condition you. I'm not doing a very good job, because the other day in the Oval Office, when the press pool came in, I was asked about this -- the series of questions -- a question on Social Security with these different aspects to it. And I said, I'm not going to negotiate with myself. I will negotiate at the appropriate time with the law writers. So, thank you for trying. The principles I laid out in the course of the campaign and the principles we laid out in the recent economic summit are still the principles I believe in. That is, nothing will change for those near our Social Security payroll. You were the one that asked me whether the payroll tax, if I'm not mistaken, will not go up. And I know there's the big definition about what that means. Well, again, I will repeat -- don't bother to ask me. Or, you can ask me. I can't tell you what to ask. That's not the holiday spirit. But I'm -- it is all part of trying to get me to set the parameters -- you know, apart from the Congress, which is not a good way to get substantive reform done. Krugman joins us on the line now, columnist for The New York Times, professor of economics at Princeton University, his latest book, The Great Unraveling: Losing Our Way in the New Century, a collection of his Times pieces. Welcome to Democracy Now! PAUL KRUGMAN: Good morning. PAUL KRUGMAN: This is a -- this is a unique excuse. I mean, I got to give him some credit. He says, Mr. President, your stuff doesn't add up. You're saying that two minus one equals four. What are you going to throw in? He says, don't get me to try to negotiate with myself. This is new. The important thing to say here is that Social Security is way down on the list of problems we have got. If you were going to take a look at just the budget, we have a huge, immediate problem on the deficit about which Bush intends to do nothing, really. We have a very serious problem on Medicare and Medicaid, which is a big issue. Social Security is the bright spot. It has maybe some mild financial problems, several decades out, and here we are -- he wants a crisis there, partly to distract from the very real crises in other places, and there you go. Because it's not just President Bush. If he was raising questions about it with a little megaphone on the steps of the White House, it would not have the kind of effect it was having without all of the media, it seems, amplifying the idea that Social Security is broken. It's bankrupt. PAUL KRUGMAN: Right. And of course, that's really a question about the media, not about Social Security. Social Security is a program which has been traditionally run. It looks like a retirement fund, and it is not exactly. What it really is is a government program with a dedicated tax. We take the payroll tax and it's used to pay benefits to retirees. And 20-plus years ago, the commission led by Alan Greenspan said, you know, we are going to have this problem as the baby boomers reach retirement age. We will have a higher ratio of retirees to workers, and we better get ready for it. Social Security, the payroll tax was increased. There were some other things, a small rise in the retirement age set in motion. So that Social Security would run a surplus, which would be used to accumulate a trust fund, and this would tithe us over, some ways into the aging of the population. And that on its own accounting is working just fine. I mean, one of the things that we need to know is that the estimates of the day at which the trust fund runs out, just keep on receding further into the future, because the program is doing so well at running surpluses. So, ten years ago, people said it was going to run out in 2029. Now the official estimate is 2042. Realistically, it's probably going to go well into the second half of the century. Now how does this become a crisis? Well it becomes a crisis by changing the rules. By saying, oh, well, actually, that surplus that we're running because of the tax increase that was designed to prolong the life of Social Security, that's not real. Because it's invested in government bonds which are a perfectly good asset, for anybody else, but not for the Social Security administration. And so, there was a real crisis that people saw in the 1980's. They dealt with it. The solution worked very well, but because this administration, because the Republican party doesn't want Social Security to remain, because they have always wanted to get rid of it since Franklin Roosevelt, they have decided to redefine the rules so as to call it a crisis when realistically, we have a huge budget problem, but that has nothing to do with Social Security. take a break. We're talking to New York Times columnist, Princeton University professor, Paul Krugman. [break] York Times. He teaches at Princeton University. His latest book, The Great Unraveling. We're talking about Social Security and other issues raised by President Bush in his 17th news conference yesterday. You talked about the real problem with the budget. I want to get to that in a minute, but what about the issue of, you said, this is really a problem with how Social Security is being conveyed, not so much with President Bush as with the media? PAUL KRUGMAN: Yeah. This is an issue where at the very least there are -- there's great dissension among people who have -- there is by no means a consensus among people who actually know something about the subject that there is a Social Security problem and certainly no consensus, there is a crisis. This is a front burner issue. But if you got your news from TV or, to a large extent, even the newspapers, you would never know that. The reporting has simply bought into the White House spin, and people who offer a different point of view are simply not considered, you know, just not part of the discussion. It's kind of like a -- well it's like the threat from Iraq, to take a random analogy. PAUL KRUGMAN: I think the thing to do is to -- I mean, certainly what I will be doing once I'm back full time at the Times is keep on hammering what the realities are and also on the fact that other countries have actually gone down the road that the Bush administration wants us to go down and the results have not been happy. So, to just say, look, this is where -- this is a phony solution to a phony crisis, and hope that at least we can get some traction. But I have to say it's pretty frustrating. You cannot get the alternative view -- which happens to be the majority of view that people who have actually studied the subject -- just can't get it on the air. its impact? PAUL KRUGMAN: Not sure what it has to do with Social Security, but we are having a -- look, the United States is running huge twin deficits. The federal government is borrowing $1 billion a day or so for the operations. The United States as a whole is borrowing $1.5 billion to pay for imports. Those can't go on forever. It's a law that says that things that cannot go on forever don't, and it appears that the world is finally looking at it and saying, Gee, we don't see this changing, and so, the money flows are starting to dry up. The dollar is falling. We don't know how it plays out. If this was a Third World country, and you had the numbers we have, you would say, Oh, my God, start stocking up on canned goods, because we look by many of the numbers worse than places like Argentina or Indonesia. But it is the United States. We get a lot of the benefit of the doubt. The debts are in dollars, which is some protection, having the debts in our own currency. But it's going to be -- it just adds to the difficulties. where do you see the crisis in the budget really is? PAUL KRUGMAN: Well, if you look at why are we -- why have we gone from surpluses to deficits? The answer is about one-quarter, roughly -- roughly, one-quarter of it is extra defense spending. Three-quarters is a plunge in revenues. And the plunge in revenues is -- a large part of it is directly the result of the Bush tax cuts. A lot of the rest we don't quite understand. It's capital gains that were a big thing in the late 1990s that dried up. Probably an increase in tax evasion and avoidance because of the political climate is favorable to that. We don't really know. But the point is, what's really happening is we're just not bringing enough tax revenue to pay for the operations of government right now and it's -- but that's off the table. Doing something to enhance revenue is clearly, from the point of view of this White House and this current ruling party, something you just don't do. And there is really no way that I can see that the spending is going to be cut enough. So, we have a deficit, which is -- which our political system is now unwilling to be realistic, unwilling to contemplate doing what has to be done to bring it down significantly. tax cuts to be made permanent. Your response to that? PAUL KRUGMAN: Well, then the question is what -- is he prepared to be honest and say that And we're going to slash Medicare benefits, slash Social Security benefits, not for people 30 years from now but people in the near term? Because you can't run deficits this size indefinitely, and you can't cut these deficits significantly without either raising taxes or making big cuts where the money is, and this -- the federal government is basically -- as number of people have said, it's basically a big insurance company with a side business in national defense. Aside from Medicare, Medicaid, Social Security and national defense, there just isn't much there. So the only way you can really pay for bringing the deficit down significantly is with big cuts in the programs that people have come to count on in their lives. occupation of Iraq on the budget in this country? PAUL KRUGMAN: Well, it's a -- I mean, roughly speaking, it's about a third of a Vietnam. That is, you are looking at - although it may be getting up to half of Vietnam, given some of the later cost estimates. It's a big expense. It's dwarfed in importance as a source of lost revenue by the tax cuts. Roughly speaking, the tax cuts are -- this past fiscal year, the tax cuts were responsible for about $270 billion of lost revenue, and the cost of the Iraq war probably was $70 billion or $80 billion. It's a little bit hard to figure out. It's a big thing, just adds to the fire, adds to the problems, but you know, I know people on -- liberals, particularly people who are horrified by the war would like to make it the root of all evil, but the truth is that on the fiscal side, it's a secondary source, compared with big tax cuts for people with very high incomes. Security -- exactly who profits right now from this debate? PAUL KRUGMAN: Well, that's -- we don't -- you know, since we don't have specifics, we don't know. I mean, what the Social Security privatization would do probably in the first place is it would probably end up removing a lot of the security features in Social Security. So that people -- you know, as it stands now, Social Security is much more than just a retirement program. It's a disability program. The way the benefits are structured tends to protect people against poverty. So, people -- the worst off would tend to be hurt and people who would have been fine without Social Security will do better, probably, as a result. Then the big question is, if we get these private accounts, how are they going to be handled? They are now saying, Oh, well, we'll put them in index funds which will generate almost no business, but now we hearing that will be for starters and then they'll relax the rules. There will be enormous lobbying pressure to relax the rules so that Wall Street gets a piece of the action, so it generates commissions. It privatized systems, they generate large commissions for the investment industry. They typically -- the operating costs are typically around 20 times as high as the operating costs of Social Security. And those are -- that all represents business for Wall Street. that we could look to as examples, that have gone through privatization? PAUL KRUGMAN: The stories -- the country that people like to point to is Chile. But what we're told is a myth about Chile. They privatized their retirement system, and lived happily ever after. The reality is that the returns on accounts of not been very good. Considering the -- you know, the fees have absorbed a large part, about probably 20% of the money put in. The other thing is that the system doesn't do the job of protecting people against poverty. Now, the good news for Chile is that from the beginning, they had a clause in there that said that the government steps in and supplements pensions if people don't have enough income to live on, basically, and that's what happens. The government ends up paying a lot of support. So, instead -- it isn't really -- they privatized it in part but it turned into a big expensive poverty support program in addition. So it just isn't doing the things that people claim it did. Britain has had a system of private pensions, and it's reaching the -- there was a big commission study, the Pensions Commission in Britain released a study in October saying that we're going to have a lot of poor older people that basically poverty among the elderly, which, in Britain as in the United States, had been greatly reduced by social insurance programs, is staging a comeback, and we're going to need to do a lot to help them out. So, these -- again, the fees to investment companies eat up a lot of the returns. So, you know, these systems are not -- they don't have the virtues that people claim for them and they actually turn out to do a lousy job of providing for people's retirement. touted as a success and it isn't. What about looking north to Canada? This is on the issue of health insurance, but how often in the media it is talked about as a complete failure, and what do you think of that? PAUL KRUGMAN: Well, the Canadians don't think so. Their health system is very popular. What is true is that the very best medical care in the U.S. is the best in the world. If you have a very good insurance program, if you are covered through your company in a way that's generous, then, the U.S. probably has somewhat better health care for you than you would get in Canada, although I actually probably don't want to say this, but the system that seems to be terrific on all dimensions is France. But anyway, the Canadian system at the very highest end is maybe slightly worse than ours. But large numbers of Americans don't get the best we can offer. In fact, the health insurance is -- the system of company-provided health insurance is cracking. The number of people in it is steadily declining. And so, we actually don't get very good coverage for many Americans. And that shows in really lousy health returns. The other thing, it's incredibly expensive. There's the myth about the efficiency of the private sector, which is true in some things, but it isn't when it comes to health insurance. In fact, the U.S. system is about twice as expensive per person as anyone else's, and we get worse results because we have basically insurance companies spending a lot of money, going to great efforts, in an effort not to cover people. All of which is wasted effort from the view of society. When you have a single-payer system, like in Canada, that doesn't happen. France, if you would dare to take it on. PAUL KRUGMAN: Just so to say that the French have a single-payer health care system. A lot of the details are different, but basically it's national health insurance. The difference between them and most other advanced countries is they actually fund it better. I mean, they -- the complaints that people have about -- the British system is the one that people say provides poor care, and apparently it largely does because the British don't spend enough money on it. The French do spend enough money on national health care and it's excellent. Infant mortality is much higher in the U.S. than it is in other advanced countries. Life expectancy is lower than it is in other advanced countries. And here we are claiming, saying, Yes, we have the best system in the world and look at how bad those other guys are. Let me tell you, when it comes to life and death, we don't do very well. us. Do you think that President Bush understands this to the point where -- this is why he vilifies France? PAUL KRUGMAN: I don't think so -- I think they have no idea. No. I doubt it. I think they -- he just has the -- I think our leadership is very insular. They just believe everything American must be best because they don't know what goes on elsewhere. Way in the New Century, columnist for The New York Times and Princeton University economist, joining us. === Subject: Re: Question about President's Social Security plan > Why not just level with the people and tell them Social Security is an > unconstitutional use of their money and in 25 years that will > cease? There's nothing unconstitutional about social security. Paul Krugman on Social Security, the Decline of the Dollar and Healthcare ------------------------------------------------------------------------ New York Times columnist and Princeton economics professor, Paul Krugman discusses President Bush's Social Security plan, the devaluation of the dollar and the healthcare debate. [includes rush transcript] ------------------------------------------------------------------------ The Bush press conference yesterday wasn't only on international issues. Several reporters questioned the president on what many see as one of the premiere domestic issues now facing the country: social security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking out an explicit, principled position in favor of dodging the question. Here is one of the exchanges Bush had with reporters when asked about his social security plan. That was President Bush, well, not answering a question on Social Security. We are joined now by New York Times columnist Paul Krugman. He has been writing a lot on this issue. One of his latest columns is called Buying into Failure, where he accuses the Bush administration of trying to convert Social Security into a giant 401(k). *Paul Krugman, New York Times columnist and Professor of Economics at Princeton University. His latest book The Great Unraveling: Losing Our Way In The New Century is a collection of his New York Times columns. Bush's news conference yesterday, the Bush news conference wasn't only on international issues. Several reporters questioned the president on what many see as one of the premier domestic issues now facing the country. Social Security. But while reporters asked many questions, the president's answers were, well, evasive. As one analyst put it, Bush seemed intent on staking a principled position while dodging the question. Here is one of the exchanges Bush had with reporters when asked about the Social Security plan. reform the top of your domestic agenda for a second term. You have been talking extensively about the benefits of private accounts, but by most estimations, private accounts may leave something for young workers at the end, but wouldn't do much to solve the overall financial problem with social security. I'm just wondering, as you promote the private accounts, why aren't you talking about the tough measures that need to be taken to preserve Social Security such as increase the retirement age, cutting benefits or means testing for Social Security? GEORGE W. BUSH: I appreciate the question. Let me put the Social Security issue in proper perspective. It is a very important issue, but it's not the only issue - very important issue, we'll be dealing with. I expect the Congress to bring forth meaningful tort reform. I want the legal system reformed in a way that we can -- we are competitive in the world. I will be talking about the budget, of course. There's a lot of concern in the financial markets about our deficits, short-term and long-term deficits. The long-term deficit is caused by some of the entitlement programs, the unfunded liabilities inherent in the entitlement programs. I will push on an education agenda. No doubt in my mind that the No Child Left Behind Act is meaningful, a real reform having real results. And I look forward to strengthening No Child Left Behind. Immigration reform is also very important agenda item as we move forward. But Social Security, as well, is a big item. I campaigned on it, as you are painfully aware, since you had to suffer through many of my speeches. I didn't duck the issue like others have done in the past. I said this is a vital issue, and we need to work together to solve it. Now, the temptation is going to be, by well-meaning people such as yourself, John, and others here as we run up to the issue, to get me to negotiate with myself in public to say, you know, what's this mean, Mr. President? What's that mean? I'm not going to do that. I don't get to write the law. I'll propose a solution at the appropriate time, but the law will be written in the halls of Congress. I will negotiate with them, with the members of Congress, and they will want me to start playing my hand. Will you accept this, will you not accept that, why don't you do this hard thing, why don't you do that. I recognize, this is going to be a decision that requires difficult choices, John. Inherent in your question I do recognize that, you bet I do. Otherwise, it would have been done. So, I am just -- I just want to condition you. I'm not doing a very good job, because the other day in the Oval Office, when the press pool came in, I was asked about this -- the series of questions -- a question on Social Security with these different aspects to it. And I said, I'm not going to negotiate with myself. I will negotiate at the appropriate time with the law writers. So, thank you for trying. The principles I laid out in the course of the campaign and the principles we laid out in the recent economic summit are still the principles I believe in. That is, nothing will change for those near our Social Security payroll. You were the one that asked me whether the payroll tax, if I'm not mistaken, will not go up. And I know there's the big definition about what that means. Well, again, I will repeat -- don't bother to ask me. Or, you can ask me. I can't tell you what to ask. That's not the holiday spirit. But I'm -- it is all part of trying to get me to set the parameters -- you know, apart from the Congress, which is not a good way to get substantive reform done. Krugman joins us on the line now, columnist for The New York Times, professor of economics at Princeton University, his latest book, The Great Unraveling: Losing Our Way in the New Century, a collection of his Times pieces. Welcome to Democracy Now! PAUL KRUGMAN: Good morning. PAUL KRUGMAN: This is a -- this is a unique excuse. I mean, I got to give him some credit. He says, Mr. President, your stuff doesn't add up. You're saying that two minus one equals four. What are you going to throw in? He says, don't get me to try to negotiate with myself. This is new. The important thing to say here is that Social Security is way down on the list of problems we have got. If you were going to take a look at just the budget, we have a huge, immediate problem on the deficit about which Bush intends to do nothing, really. We have a very serious problem on Medicare and Medicaid, which is a big issue. Social Security is the bright spot. It has maybe some mild financial problems, several decades out, and here we are -- he wants a crisis there, partly to distract from the very real crises in other places, and there you go. Because it's not just President Bush. If he was raising questions about it with a little megaphone on the steps of the White House, it would not have the kind of effect it was having without all of the media, it seems, amplifying the idea that Social Security is broken. It's bankrupt. PAUL KRUGMAN: Right. And of course, that's really a question about the media, not about Social Security. Social Security is a program which has been traditionally run. It looks like a retirement fund, and it is not exactly. What it really is is a government program with a dedicated tax. We take the payroll tax and it's used to pay benefits to retirees. And 20-plus years ago, the commission led by Alan Greenspan said, you know, we are going to have this problem as the baby boomers reach retirement age. We will have a higher ratio of retirees to workers, and we better get ready for it. Social Security, the payroll tax was increased. There were some other things, a small rise in the retirement age set in motion. So that Social Security would run a surplus, which would be used to accumulate a trust fund, and this would tithe us over, some ways into the aging of the population. And that on its own accounting is working just fine. I mean, one of the things that we need to know is that the estimates of the day at which the trust fund runs out, just keep on receding further into the future, because the program is doing so well at running surpluses. So, ten years ago, people said it was going to run out in 2029. Now the official estimate is 2042. Realistically, it's probably going to go well into the second half of the century. Now how does this become a crisis? Well it becomes a crisis by changing the rules. By saying, oh, well, actually, that surplus that we're running because of the tax increase that was designed to prolong the life of Social Security, that's not real. Because it's invested in government bonds which are a perfectly good asset, for anybody else, but not for the Social Security administration. And so, there was a real crisis that people saw in the 1980's. They dealt with it. The solution worked very well, but because this administration, because the Republican party doesn't want Social Security to remain, because they have always wanted to get rid of it since Franklin Roosevelt, they have decided to redefine the rules so as to call it a crisis when realistically, we have a huge budget problem, but that has nothing to do with Social Security. take a break. We're talking to New York Times columnist, Princeton University professor, Paul Krugman. [break] York Times. He teaches at Princeton University. His latest book, The Great Unraveling. We're talking about Social Security and other issues raised by President Bush in his 17th news conference yesterday. You talked about the real problem with the budget. I want to get to that in a minute, but what about the issue of, you said, this is really a problem with how Social Security is being conveyed, not so much with President Bush as with the media? PAUL KRUGMAN: Yeah. This is an issue where at the very least there are -- there's great dissension among people who have -- there is by no means a consensus among people who actually know something about the subject that there is a Social Security problem and certainly no consensus, there is a crisis. This is a front burner issue. But if you got your news from TV or, to a large extent, even the newspapers, you would never know that. The reporting has simply bought into the White House spin, and people who offer a different point of view are simply not considered, you know, just not part of the discussion. It's kind of like a -- well it's like the threat from Iraq, to take a random analogy. PAUL KRUGMAN: I think the thing to do is to -- I mean, certainly what I will be doing once I'm back full time at the Times is keep on hammering what the realities are and also on the fact that other countries have actually gone down the road that the Bush administration wants us to go down and the results have not been happy. So, to just say, look, this is where -- this is a phony solution to a phony crisis, and hope that at least we can get some traction. But I have to say it's pretty frustrating. You cannot get the alternative view -- which happens to be the majority of view that people who have actually studied the subject -- just can't get it on the air. its impact? PAUL KRUGMAN: Not sure what it has to do with Social Security, but we are having a -- look, the United States is running huge twin deficits. The federal government is borrowing $1 billion a day or so for the operations. The United States as a whole is borrowing $1.5 billion to pay for imports. Those can't go on forever. It's a law that says that things that cannot go on forever don't, and it appears that the world is finally looking at it and saying, Gee, we don't see this changing, and so, the money flows are starting to dry up. The dollar is falling. We don't know how it plays out. If this was a Third World country, and you had the numbers we have, you would say, Oh, my God, start stocking up on canned goods, because we look by many of the numbers worse than places like Argentina or Indonesia. But it is the United States. We get a lot of the benefit of the doubt. The debts are in dollars, which is some protection, having the debts in our own currency. But it's going to be -- it just adds to the difficulties. where do you see the crisis in the budget really is? PAUL KRUGMAN: Well, if you look at why are we -- why have we gone from surpluses to deficits? The answer is about one-quarter, roughly -- roughly, one-quarter of it is extra defense spending. Three-quarters is a plunge in revenues. And the plunge in revenues is -- a large part of it is directly the result of the Bush tax cuts. A lot of the rest we don't quite understand. It's capital gains that were a big thing in the late 1990s that dried up. Probably an increase in tax evasion and avoidance because of the political climate is favorable to that. We don't really know. But the point is, what's really happening is we're just not bringing enough tax revenue to pay for the operations of government right now and it's -- but that's off the table. Doing something to enhance revenue is clearly, from the point of view of this White House and this current ruling party, something you just don't do. And there is really no way that I can see that the spending is going to be cut enough. So, we have a deficit, which is -- which our political system is now unwilling to be realistic, unwilling to contemplate doing what has to be done to bring it down significantly. tax cuts to be made permanent. Your response to that? PAUL KRUGMAN: Well, then the question is what -- is he prepared to be honest and say that And we're going to slash Medicare benefits, slash Social Security benefits, not for people 30 years from now but people in the near term? Because you can't run deficits this size indefinitely, and you can't cut these deficits significantly without either raising taxes or making big cuts where the money is, and this -- the federal government is basically -- as number of people have said, it's basically a big insurance company with a side business in national defense. Aside from Medicare, Medicaid, Social Security and national defense, there just isn't much there. So the only way you can really pay for bringing the deficit down significantly is with big cuts in the programs that people have come to count on in their lives. occupation of Iraq on the budget in this country? PAUL KRUGMAN: Well, it's a -- I mean, roughly speaking, it's about a third of a Vietnam. That is, you are looking at - although it may be getting up to half of Vietnam, given some of the later cost estimates. It's a big expense. It's dwarfed in importance as a source of lost revenue by the tax cuts. Roughly speaking, the tax cuts are -- this past fiscal year, the tax cuts were responsible for about $270 billion of lost revenue, and the cost of the Iraq war probably was $70 billion or $80 billion. It's a little bit hard to figure out. It's a big thing, just adds to the fire, adds to the problems, but you know, I know people on -- liberals, particularly people who are horrified by the war would like to make it the root of all evil, but the truth is that on the fiscal side, it's a secondary source, compared with big tax cuts for people with very high incomes. Security -- exactly who profits right now from this debate? PAUL KRUGMAN: Well, that's -- we don't -- you know, since we don't have specifics, we don't know. I mean, what the Social Security privatization would do probably in the first place is it would probably end up removing a lot of the security features in Social Security. So that people -- you know, as it stands now, Social Security is much more than just a retirement program. It's a disability program. The way the benefits are structured tends to protect people against poverty. So, people -- the worst off would tend to be hurt and people who would have been fine without Social Security will do better, probably, as a result. Then the big question is, if we get these private accounts, how are they going to be handled? They are now saying, Oh, well, we'll put them in index funds which will generate almost no business, but now we hearing that will be for starters and then they'll relax the rules. There will be enormous lobbying pressure to relax the rules so that Wall Street gets a piece of the action, so it generates commissions. It privatized systems, they generate large commissions for the investment industry. They typically -- the operating costs are typically around 20 times as high as the operating costs of Social Security. And those are -- that all represents business for Wall Street. that we could look to as examples, that have gone through privatization? PAUL KRUGMAN: The stories -- the country that people like to point to is Chile. But what we're told is a myth about Chile. They privatized their retirement system, and lived happily ever after. The reality is that the returns on accounts of not been very good. Considering the -- you know, the fees have absorbed a large part, about probably 20% of the money put in. The other thing is that the system doesn't do the job of protecting people against poverty. Now, the good news for Chile is that from the beginning, they had a clause in there that said that the government steps in and supplements pensions if people don't have enough income to live on, basically, and that's what happens. The government ends up paying a lot of support. So, instead -- it isn't really -- they privatized it in part but it turned into a big expensive poverty support program in addition. So it just isn't doing the things that people claim it did. Britain has had a system of private pensions, and it's reaching the -- there was a big commission study, the Pensions Commission in Britain released a study in October saying that we're going to have a lot of poor older people that basically poverty among the elderly, which, in Britain as in the United States, had been greatly reduced by social insurance programs, is staging a comeback, and we're going to need to do a lot to help them out. So, these -- again, the fees to investment companies eat up a lot of the returns. So, you know, these systems are not -- they don't have the virtues that people claim for them and they actually turn out to do a lousy job of providing for people's retirement. touted as a success and it isn't. What about looking north to Canada? This is on the issue of health insurance, but how often in the media it is talked about as a complete failure, and what do you think of that? PAUL KRUGMAN: Well, the Canadians don't think so. Their health system is very popular. What is true is that the very best medical care in the U.S. is the best in the world. If you have a very good insurance program, if you are covered through your company in a way that's generous, then, the U.S. probably has somewhat better health care for you than you would get in Canada, although I actually probably don't want to say this, but the system that seems to be terrific on all dimensions is France. But anyway, the Canadian system at the very highest end is maybe slightly worse than ours. But large numbers of Americans don't get the best we can offer. In fact, the health insurance is -- the system of company-provided health insurance is cracking. The number of people in it is steadily declining. And so, we actually don't get very good coverage for many Americans. And that shows in really lousy health returns. The other thing, it's incredibly expensive. There's the myth about the efficiency of the private sector, which is true in some things, but it isn't when it comes to health insurance. In fact, the U.S. system is about twice as expensive per person as anyone else's, and we get worse results because we have basically insurance companies spending a lot of money, going to great efforts, in an effort not to cover people. All of which is wasted effort from the view of society. When you have a single-payer system, like in Canada, that doesn't happen. France, if you would dare to take it on. PAUL KRUGMAN: Just so to say that the French have a single-payer health care system. A lot of the details are different, but basically it's national health insurance. The difference between them and most other advanced countries is they actually fund it better. I mean, they -- the complaints that people have about -- the British system is the one that people say provides poor care, and apparently it largely does because the British don't spend enough money on it. The French do spend enough money on national health care and it's excellent. Infant mortality is much higher in the U.S. than it is in other advanced countries. Life expectancy is lower than it is in other advanced countries. And here we are claiming, saying, Yes, we have the best system in the world and look at how bad those other guys are. Let me tell you, when it comes to life and death, we don't do very well. us. Do you think that President Bush understands this to the point where -- this is why he vilifies France? PAUL KRUGMAN: I don't think so -- I think they have no idea. No. I doubt it. I think they -- he just has the -- I think our leadership is very insular. They just believe everything American must be best because they don't know what goes on elsewhere. Way in the New Century, columnist for The New York Times and Princeton University economist, joining us. === Subject: Re: Question about President's Social Security plan Why not just level with the people and tell them Social Security is an unconstitutional use of their money and in 25 years that will cease? Liberals and those they've made dependent on the federal government don't care about Social Security's unconstitutionality; as the childish people they are, they're delighted that Government can and will do all kinds of things to meet human needs. It is for this reason that for decades Social Security has been treated by politicians in DC as something that people hold sacred. (The dopiest of Dems even take sacredness further: they worship their God, FDR.) === Subject: Re: Question about President's Social Security plan > Why not just level with the people and tell them Social Security is an > unconstitutional use of their money and in 25 years that will cease? > Liberals and those they've made dependent on the federal government > don't care about Social Security's unconstitutionality; as the childish > people they are, they're delighted that Government can and will do > all kinds of things to meet human needs. It is for this reason that > for decades Social Security has been treated by politicians in DC as > something that people hold sacred. > (The dopiest of Dems even take sacredness further: they worship their > God, FDR.) Dave was raised by baboons. He shows us all the bankruptcy of compassionate conservatism. === Subject: Re: Question about President's Social Security plan Alias: Smith or Jones says... >Why not just level with the people and tell them Social Security is an >unconstitutional use of their money and in 25 years that will cease? So, all >you nice folks that have been letting the government have some walking >around cash better start saving now for that rainy day coming up 25 years >from now. The way I see it, Bush's social security plan is like one of those paradoxical science fiction stories about predicting the future. The hero foresees some great catastrophe, and so takes steps to prepare for it. Ironically, those steps turn out to be exactly what *causes* the catastrophe. Except that it's not haplessness, it is intentional. Bush is actively taking steps to *insure* that social security goes bankrupt. -- Daryl McCullough Ithaca, NY === Subject: Re: Question about President's Social Security plan : Alias: Smith or Jones says... : : >Why not just level with the people and tell them Social Security is an : >unconstitutional use of their money and in 25 years that will cease? So, all : >you nice folks that have been letting the government have some walking : >around cash better start saving now for that rainy day coming up 25 years : >from now. : : The way I see it, Bush's social security plan is like one of those : paradoxical science fiction stories about predicting the future. The : hero foresees some great catastrophe, and so takes steps to prepare : for it. Ironically, those steps turn out to be exactly what *causes* : the catastrophe. : : Except that it's not haplessness, it is intentional. Bush is actively : taking steps to *insure* that social security goes bankrupt. : : -- : Daryl McCullough : Ithaca, NY : Bush Smush, who cares. They're all in it together. Scrap it and move on. -- Who are these guys? If the world were a logical place, men would ride horses sidesaddle Smith or Jones === Subject: A Quantum Poem for Xmas A Quantum Poem for Xmas --------------- I wonder if science shall ever see, a quantum discrete as a tree, Alas, the answer no must be, For what science views is energy, Where, as discrete, Quantum Mystics see in their symmetric reverie the integral over r of nm0c. === Subject: Re: A Quantum Poem for Xmas > A Quantum Poem for Xmas > --------------- > I wonder if science shall ever see, > a quantum discrete as a tree, > Alas, the answer no must be, > For what science views is energy, > Where, as discrete, Quantum Mystics see > in their symmetric reverie > the integral over r of nm0c. not too bad considering where it came from. I wonder whether this is a poem. is it? do you think that a poem is that which seems to rhyme? let's say it should be admired, not for its rhymes, not for any reasons of form, but for its *content*, the depth of its meaning. remember this is probably from the same country as jingle bells and dreaming of a white krismes which are infinitely, immensely, unspeakably more stupid. don't you think so? === Subject: Re: A Quantum Poem for Xmas >> A Quantum Poem for Xmas >> --------------- >> I wonder if science shall ever see, >> a quantum discrete as a tree, >> Alas, the answer no must be, >> For what science views is energy, >> Where, as discrete, Quantum Mystics see >> in their symmetric reverie >> the integral over r of nm0c. >not too bad considering where it came from. I wonder whether this is a >poem. is it? do you think that a poem is that which seems to rhyme? Actually pretty excellent especially where it came from. America is a country of unsophisticated and certainly unpretentious tastes as yet. This is a takeoff on a Bennett Cerf parody of a Joyce (?) poem. >let's say it should be admired, not for its rhymes, not for any reasons >of form, but for its *content*, the depth of its meaning. The purpose of the poem was not its artistic merit but its content and depth of meaning. > remember this >is probably from the same country as jingle bells and dreaming of a >white krismes which are infinitely, immensely, unspeakably more >stupid. don't you think so? Remembering that America is the country that pulled Europe's cujones out of the fire in the first and second world wars at enormous cost to itself and its people, I consider that its tastes in popular music can be forgiven in the worst cases and considerably enjoyed in best cases. === Subject: Re: A Quantum Poem for Xmas > A Quantum Poem for Xmas > --------------- > I wonder if science shall ever see, > a quantum discrete as a tree, Hopeless ignorant idiot. SCANSION! Zick Limerick ------------- There once was an old idiot who had some poor idea of how mum Went to bed With dread Because Lester suckled her left bum cheek in the night. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: A Quantum Poem for Xmas