mm-1077
===
Subject: Re: terms in Math
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iBHMLmj09356;
>Can anyone tell me the URL with pages devoted to math \
terms.
One such is http://mathworld.wolfram.com/
===
Subject: Re: coverings of a Mobius band
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iBHMLmT09372;
>Are the even degree covers of a Mobius band annulus(es)? Are
the odd degree
covers of a Mobius band, Mobius bands again? What is the
universal cover of
a Mobius band?
Yes, yes, and R x [-1, 1]. One can imagine a strip of paper
with
n half-twists before gluing the ends as the total space of the
degree n cover of the Mobius band. The strip of paper is
I x [-1, 1], and the gluing map for taping the ends is the
homeomorphism (-1)^n * - : [-1, 1] --> [-1, 1], so we get
an annulus for n even and a Mobius strip for n odd. For the
universal cover, imagine an in\finite strip with \
in\finitely
many half-twists.
Todd Trimble
===
Subject: Re: The Possible Cure For AIDS
in part:
> There are no As, Gs, 4s, \
Os,
>>The G is gimmel the 3 rd letter of the Hebrew alphabet.
>>The vowels (mplicit in old Hebrew but made explicit by the
Masorites)
>>include an ah sound and a oh sound.
>AFAIK the Torah codes are never done with the vowels.
Thats quite true. Including vowels makes it harder to \
\find
matches. But
if someone wanted to \find English words in the Tanakh, the
standard
convention is, of course, Aleph for A and Ayin for O. As for
the number
404, two letters would represent that in standard Hebrew
numeric
notation: Tau and Daleth.
But Hebrew has a word for silver, although *ancient* Hebrew
hardly had a
word for oxygen, even if it certainly has one today.
Actually, we should be asking what letters of the Hebrew
alphabet are
supposed to stand for and !
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: The Possible Cure For AIDS
> But Hebrew has a word for silver, although *ancient* Hebrew
hardly had a
Kessef.
> word for oxygen, even if it certainly has one today.
Khamtzan which means sour-er. This corresponds to the German
Saurstuff.
> Actually, we should be asking what letters of the Hebrew
alphabet are
> supposed to stand for and !
There is a typefont used to crossreference passages in the
Talmud to the
Shulkhan Arooch. It looks like superscripts because of the
way it is
printed. This was originated about 1500 of the common era.
Bob Kolker
===
Subject: Re: The Possible Cure For AIDS
in part:
>There are no As, Gs, 4s, \
Os, etc. in Hebrew. Did you
transliterate
>these according to some arbitrary scheme, or did you search
for Hebrew
>letter strings?
Not that it matters, of course.
But while were talking about a cure for AIDS...
Some years back, there were news stories about how, for AIDS
research,
modi\fied mice were created with human immune systems. This was
done by
taking cells from human fetuses.
Naturally, this was controversial because of the abortion
issue.
I noted that nobody cares about mouse fetuses. If you can \fix
a mouse so
that it _can_ get AIDS by giving it a human beings immune
system, it
would seem you could \fix a human so that he \
cant get AIDS by
giving him
a mouses immune system.
There were probably very good reasons why this couldnt
_really_ be
done, but I had thought it worth mentioning.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Beals conjecture
> => A large prize is offered by banker Andrew Beal for a
solution to
> => the Beal Conjecture: the equation x^p + y^q = z^r has no
solutions
> => for p, q, r > 2 and coprime integers x, y, z.
> => => Sorry if this has been discussed here - my only
justi\fication
> => is that I just recently discovered this group but I am
curious to
> => know if Wiles proof of FLT also covers the Beal
Conjecture
> => Or have any counter-examples been found?
Wiles proof covered the case p=q=r and relaxed the coprime
requirement
for x, y, & z. IE: There is no integer solution when p=q=r
whatever
the coprimality of x, y, & z.
tom
--
We have discovered a therapy ( NOT a cure )
for the common cold. Play tuba for an hour.
===
Subject: Mathforge.net :: Near-numbers, autonomic computing,
John
Derbyshire, and Church-Turing
posting-account=Jy65eAwAAADVuRECxXfbsbHI5uTpc8FY
The Latest Math News from Mathforge.net
http://mathforge.net
****An invitation to additive prime number theory****
A.V. Kumchev and D.I. Tolev have compiled a short document
entitled An
Invitation to Additive Prime Number Theory[~60pp, pdf]. The
document
serves as an introductory guide to graduate-level students
on...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=981
****Are there encoded messages in the Bible?****
researchers both supporting and denying the statistical
evidence for
Ôhidden messages found in the Old Testament \
tell their
tales. Some...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=974
****Near-numbers: the new Ôlimit****
Theres a very interesting paper by Frank J Swenton of
Middlebury
College called Limits and the System of Near-Numbers[19pp,
pdf]. What
seemed at \first glance (at the title and abstract) like an
uninspired...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=970
****Introduction to autonomic computing****
While not itself mathematical in nature, the concept is built
around
ideas garnered from areas of arti\ficial intelligence research
and it is
easy to see that autonomic computing could have
applications...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=969
****Derbyshires Diary****
John Derbyshire, author of Prime Obsession, has a
mathematical problem
accompanying each of his Diary entries located in his Web
Journalism
folder. If you sift through enough of the partisan
propaganda...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=968
****Maple 9.5 Released****
MapleSoft has released version 9.5 of their popular symbolic
and
numeric computational software suite Maple. New Features
include added
packages (optimization, logic, and root \finding), OpenMaple
access...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=967
****Mathematica 5.1 released****
The Mathematica version has jumped a tenth of a point, and
Wolfram has
added scores of new features to the new release, including
Web Services
support, a benchmarking package, string manipulation
functions,...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=966
****Quantum computers and the Church-Turing Thesis****
The original Church-Turing Thesis states that every function
which
would naturally be regarded as computable can be computed by
a Turing
Machine and Petrus H. Potgeiter mentions in his paper Zeno
Machines...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=963
****Sobering U.S. Student Math Scores****
In a disheartening follow-up to the Putnam story below, news
(Seattle
Times) outlets (New York Times)everywhere are reporting the
horrid
state of U.S. student math skills. The Organisation for
Economic...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=959
ÔMathforge ran a story about the Putnam \
Competition...
http://mathforge.net/index.jsp?page=seeReplies&messageNum=958
===
Subject: What kind of matrix can map positive element vectors
to positive
element vectors?
Hi all,
Suppose I have a matrix A, and a positive element vector x,
then y=A*x,
I want y to be also positive element vector...
What can I say about A? I want all such kinds of A?
What kinds of A can let me have both directions:
x positive elements <=> y=A*x positive elements?
===
Subject: Re: What kind of matrix can map positive element
vectors to
positive
element vectors?
> Hi all,
> Suppose I have a matrix A, and a positive element vector x,
> then y=A*x,
> I want y to be also positive element vector...
> What can I say about A? I want all such kinds of A?
> What kinds of A can let me have both directions:
> x positive elements <=> y=A*x positive elements?
Take a simple case and try to learn from it.
The unit vectors for x will pull out the columns of A.
Sure seems to say that A must at least have all of its
elements positive.
===
Subject: Re: What kind of matrix can map positive element
vectors to
positive element vectors?
> Hi all,
>
> Suppose I have a matrix A, and a positive element vector x,
>
> then y=A*x,
>
> I want y to be also positive element vector...
>
> What can I say about A? I want all such kinds of A?
>
> What kinds of A can let me have both directions:
>
> x positive elements <=> y=A*x positive elements?
>
>
>
> Take a simple case and try to learn from it.
> The unit vectors for x will pull out the columns of A.
> Sure seems to say that A must at least have all of its
> elements positive.
Necessary and suf\ficient.
===
Subject: How to determine parameter integer values such that
quadratic has
integer solutions?
posting-account=uJhfTw0AAACZ85X1hg4ZQuYw9kXQVPPG
Hi all,
In particular, Im interested in \finding the \
positive integer
values of
g such that the following quadratic in v has integer roots:
v^2 - 7v + (12 - 12g)
Evidently this requires that 1 + 48g be a perfect square. I
can have
Mathematica spit out such values, which begin with: 0, 1, 6,
11, 13,
20, 35, ...
This sequence is more conveniently summarized as
something-mod-something-else, but I forget exactly what the
two
somethings are. How to \figure this out?
cdj
===
Subject: Re: How to determine parameter integer values such
that quadratic
has integer solutions?
> In particular, Im interested in \finding the \
positive
integer values of
> g such that the following quadratic in v has integer roots:
> v^2 - 7v + (12 - 12g)
v = (7 +- sqr(49 - 48 + 48g)/2
= (7 +- sqr(1 + 48g)/2
sqr(1 + 48g) must be odd number, 2n + 1
1 + 48g = 4n^2 + 4n + 1
12g = n^2 + n = n(n + 1)
Case 12 | n. Done
Case 4 | n, not 3 | n. 3 | n+1; n = 3k - 1
Case 3 | n, not 2 | n. 4 | n+1; n = 4k - 1
Case 2 | n, not 4 | n. Not possible
Three family parametrization of solutions.
n = 12k
n = 3k - 1 provided 4 | n
n = 4k - 1 provided 3 | n
Expect some duplicates.
> Evidently this requires that 1 + 48g be a perfect square. I
can have
> Mathematica spit out such values, which begin with: 0, 1,
6, 11, 13,
> 20, 35, ...
> This sequence is more conveniently summarized as
> something-mod-something-else, but I forget exactly what the
two
> somethings are. How to \figure this out?
===
Subject: Re: How to determine parameter integer values such
that quadratic
has integer solutions?
posting-account=uJhfTw0AAACZ85X1hg4ZQuYw9kXQVPPG
The square root of 1+48g is odd... for Ôs sake \
Im blind....
===
Subject: Re: How to determine parameter integer values such
that quadratic
has integer solutions?
cdj:
Heres an outline:
We know that 1+48g is a perfect square. Since g is an
integer, 48g is
even, and 1+48g is odd. So, the square root of 1+48g is odd,
and we can
write that square root as 2n+1 for some integer n. Thus,
(2n+1)^2 = 1+48g
Expanding and simplifying,
4n^2+4n+1 = 1+48g
4n^2+4n = 48g
n^2+n = 12g
We need a little number theory here: Consider the above
equation (mod 12):
(n^2+n) (mod 12) = 0
Trying the 11 possibilities, we \find that n (mod 12) must be
0, 3, 8, or
11, that is, we must be able to write n as 12k or 12k+3 or
12k+8 or
12k+11 for some integer k. (The above condition is equivalent
to
(n^2+n) = 0 (mod 3) AND (n^2+n) = 0 (mod 4), so with some
work, we
really need only to consider 3+4 = 7 cases.)
Substituting for the \first possibility (n = 12k, that is, n is
a
multiple of 12),
n^2+n = (12k)^2+(12k) = 144k^2+12k = 12(12k^2+k)
But, n^2+n = 12g, so this case gives:
12(k^2+k) = 12g, that is,
g = 12k^2+k
The second possibility (n = 12k+3, that is, n is 3 more than
a multiple
of 12) similarly gives
n^2+n = (12k+3)^2+(12k+3) = 144k^2+84k+12 = 12(12k^2+7k+1)
12(12k^2+7k+1) = 12g, so,
g = 12k^2+7k+1
The other possibilities (n = 12k+8, n=12k+11) give after
similar
calculations,
g = 12k^2+17k+6, and
g = 12k^2+23k+11
If k > 0, then all four possibilities clearly give
nonnegative values
for g. (For k = 0, we generate the \first four values of your
sequence:
0, 1, 6, 11.)
Suppose we want to generate a list of such values: We can
exhaust all
the possibilities for g by evaluating the above four formulas
for g for
each k = 0,1,2,3,... (When writing your list, because you
need positive
integer values for g, youll need to throw away the \
\first
element of
your list, 12(0)^2+(0)=0.)
Considering the values of g generated by a particular k, we
have (clearly):
12k^2+k < 12k^2+7k+1 < 12k^2+17k+6 < 12k^2+23k+11.
So, the smallest value of g generated by k+1 is:
12(k+1)^2+(k+1) = 12k^2+25k+13 > 12k^2+23k+11
That is, the smallest value for g generated by k+1 is larger
than the
largest value generated by k.
So, we can write down a complete ordered list (a sequence
that gives the
possible solutions for g in increasing order) by writing down
the four
possibilities for g generated by 0 (in increasing order),
then the four
generated by 1, then those for 2, and so on.
I dont know how to write the sequence more compactly than \
by
writing
down the above rule.
Travis
> Hi all,
> In particular, Im interested in \finding the \
positive
integer values of
> g such that the following quadratic in v has integer roots:
> v^2 - 7v + (12 - 12g)
> Evidently this requires that 1 + 48g be a perfect square. I
can have
> Mathematica spit out such values, which begin with: 0, 1,
6, 11, 13,
> 20, 35, ...
> This sequence is more conveniently summarized as
> something-mod-something-else, but I forget exactly what the
two
> somethings are. How to \figure this out?
> cdj
===
Subject: Integral
posting-account=DH5daAwAAADTxT0WC17CRoCKZYkI-swj
Hi.
What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed
form?
===
Subject: Re: Integral
>Hi.
>What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed
form?
http://integrals.wolfram.com/ says:
RootSum[-1+#1+#1^2+#1^5 &, (Log[x-#1] / (1+2#1+5#1^4)) &]
Thomas
===
Subject: Re: Integral
> Hi.
> What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed
form?
As soon as you come up with a closed form of factorization of
x^5 + x^2 + x - 1
(one linear factor and two quadratic factors),
I will be able to tell you more.
===
Subject: Re: Integral
Mike4ty,
Ugly, I think. Factor the polynomial (warning, its
irreducible over
the integers), then apply the method of partial fractions.
Travis
> Hi.
> What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed
form?
===
Subject: Re: Integral
> Hi.
> What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed
form?
The hard part is solving the quintic. There is a real root
near 0.568544,
a
complex conjugate pair near 0.91612 +/- 0.57771 i, and
another pair near
0.622848 +/- 1.03222 i.
Once you have the factors, its an easy partial fractions
decomposition,
provided you dont mind approximate answers.
Mathematica 5.0 for Mac OS X
-- Terminal graphics initialized --
In[1]:= Integrate[1./(x^5+x^2+x-1),x]
Out[1]= 1. (-0.22894 ArcTan[0.484391 (-1.2457 + 2. x)] -
> 0.189874 ArcTan[0.865487 (1.83224 + 2. x)] +
> 0.361679 Log[0.586544 - 1. x] -
2
> 0.0641575 Log[1.45342 - 1.2457 x + x ] -
2
> 0.116682 Log[1.17302 + 1.83224 x + x ])
--
Dave Seaman
Judge Yohns mistakes revealed in Mumia Abu-Jamal ruling.
===
Subject: Galois group = A_4
The following question has been bugging me : I am trying to
come up with a
quartic polynomial whose Galois group is A_4. I know I can go
about the
business of \finding a discriminant that is the square of a
rational number,
and the resolvent cubic is irreducible. But I was wondering
if there was a
more illuminating way to geometrically come up with a quartic
polynomial.
In particular, we know A_4 has no transpositions and no
4-cycles. So, what
can I say about the quartic?
Wouldnt it be true that since there are no transpositions,
the quartic
cannot have exactly 2 real roots?
What can I deduce about the fact that the Galois group has no
4-cycles?
Tony
===
Subject: Re: Question about Presidents Social Security plan
>Yes, except that the government doesnt 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 hyperinßation. 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
doesnt
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
inßation. 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 bene\fits going out.
--
Iraq was a brilliant campaign fought with minimal
casualties, 11 September was a humiliating failure
by government to ful\fill 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 horri\fied that he was too
quick to act on doubtful intelligence re Iraq. This
is not a serious party.
===
Subject: Re: Question about Presidents Social Security plan
OrionCA says...
>Iraq was a brilliant campaign fought with minimal
>casualties, 11 September was a humiliating failure
>by government to ful\fill 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 horri\fied 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 Presidents Social Security plan
>OrionCA says...
>>Iraq was a brilliant campaign fought with minimal
>>casualties, 11 September was a humiliating failure
>>by government to ful\fill 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 horri\fied 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 ful\fill 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 horri\fied that he was too
quick to act on doubtful intelligence re Iraq. This
is not a serious party.
===
Subject: Re: Question about Presidents Social Security plan
>>Yes, except that the government doesnt 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 hyperinßation.
The government prints money, i.e. monetizes the debt, for
only two
reasons: (1) to meet the publics 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 bene\ficiaries will not
require the
printing of money. It will involve de\ficit 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
doesnt
>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
>inßation. 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 de\ficit, but only
during
the peak years of bene\fits 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 bene\fits 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 Presidents Social Security plan
>So my question is, wouldnt 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 theyd 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 doesnt 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;
theyll 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 youd get at least that and
probably
much more, paid out of the growth in the GDP between now and
retirement. In effect its a redistribution of wealth (which
should
make liberals happy but go \figure) because what you \
dont 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 ful\fill 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 horri\fied that he was too
quick to act on doubtful intelligence re Iraq. This
is not a serious party.
===
Subject: Re: Question about Presidents Social Security plan
<57u6s0tmu6hrfdaqsjirlk290r7u5p3v4l@4ax.com>
posting-account=v1V-4A0AAAD0uc5c2ERg25Qdl2W__hSu
> 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 youd 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 ßown 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 its a redistribution of wealth
(which should
Yes, in effect it is indeed nothing but a redistribution of
wealth.
But I
dont agree with the direction you seem to think it works \
in.
===
Subject: Re: Question about Presidents 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 youd 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
dont 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 aint 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 ful\fill 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 horri\fied that he was too
quick to act on doubtful intelligence re Iraq. This
is not a serious party.
===
Subject: Re: Question about Presidents 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 Cheneys 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 Presidents Social Security plan
posting-account=v1V-4A0AAAD0uc5c2ERg25Qdl2W__hSu
>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 Cheneys \
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 Bushs legacy will be to leave the
economy booming. Whether its a false
or temporary boom, wont 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 Presidents Social Security plan
posting-account=i3qD7AwAAACHjGKcE_VihY5XWtSCm1bP
This [privatize some parts of social security]
will cost $2 trillion to set up.
So my question is, wouldnt 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
youd simply be perpetuating a poor system that
by your own words remains in de\ficit, 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
bene\fits, 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 Bushs 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
inßuence and social responsibility, faddish far-left
idiocy such as Israeli divestiture gimmicks, maybe
government shareholder inßuence on politically
disfavored industries like guns and automobiles, and
so on. No normal American wants any threat of that.
===
Subject: Re: Question about Presidents Social Security plan
> A more legitimate problem with Bushs 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
> inßuence and social responsibility, faddish far-left
> idiocy such as Israeli divestiture gimmicks, maybe
> government shareholder inßuence on politically
> disfavored industries like guns and automobiles, and
> so on. No normal American wants any threat of that.
I cant imagine that political agitation for restriction of
these
investments would be con\fined 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 Presidents Social Security plan
>> A more legitimate problem with Bushs 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
>> inßuence and social responsibility, faddish far-left
>> idiocy such as Israeli divestiture gimmicks, maybe
>> government shareholder inßuence on politically
>> disfavored industries like guns and automobiles, and
>> so on. No normal American wants any threat of that.
> I cant imagine that political agitation for restriction \
of
these
>investments would be con\fined 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 Presidents Social Security plan
posting-account=v1V-4A0AAAD0uc5c2ERg25Qdl2W__hSu
> The counter-argument would be that in doing so
> youd simply be perpetuating a poor system that
> by your own words remains in de\ficit, 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 its erroneous
in this context to call 0.7 trillion over 75 years
as small. Its 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 Presidents Social Security plan
posting-account=i3qD7AwAAACHjGKcE_VihY5XWtSCm1bP
> 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
super\ficial in
our approach and simply tax more during low-bene\ficiary-number
years or
decades to better \finance bene\fits during
high-bene\ficiary-number years
or decades that follow them.
> Not looked at the budget \figures lately, have we?
Im 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 its erroneous
> in this context to call 0.7 trillion over 75 years
> as small. Its better called negligible or trivial
> or irrelevant.
Thats 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 Presidents Social Security plan
posting-account=v1V-4A0AAAD0uc5c2ERg25Qdl2W__hSu
> Maybe you have a point -- perhaps its erroneous
> in this context to call 0.7 trillion over 75 years
> as small. Its better called negligible or trivial
> or irrelevant.
> Thats 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 Bushs \fix \
involves
borrowing $2 trillion. Whats 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 Presidents Social Security plan
posting-account=i3qD7AwAAACHjGKcE_VihY5XWtSCm1bP
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 theyve made dependent on the federal
government
dont care about Social Securitys \
unconstitutionality; as
the childish
people they are, theyre 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 Presidents Social Security plan
posting-account=v1V-4A0AAAD0uc5c2ERg25Qdl2W__hSu
> Youre 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 dont 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 werent 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 doesnt believe the nice havemores would
advise something that could have bad results.
Its 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 dont 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 doesnt seem right, or American,
or a good thing at all for the long
term future.
===
Subject: Re: How to \find the extremum of the Absolute value of
a
function=?big5?Q?=EF=BC=9F?=
My method is to differentiate |Z| w.r.t y, and then subtitute
y1 and y2
into
the above equation. Finally I got a simultaneous equations
and solving for
x1 and x2.
But where confused me is that the derivative of an absolute
value seems not
exist, so my known method didnt work due to the absolute
value.
is there any other method to solve a extremum problem of an
obsolute value?
(Randy
Poe)n2
50G
> Suppose I have a complex-valued function Z, and
Z=3DZ(x1,x2,y)
> where x1,x2 and y are three real variables. I wanna |Z| has
local
> minimums at two given points y=3Dy1 and y=3Dy2, where x1
and x2 should
be
> adjusted to met this demand.
> i.e.
> Q=EF=BC=9AHow to \find x1 and x2 such that |Z| has local
minimum at two
> given points
> y1 and y2 ?
> To \find the minimimum for y=3Dy1, de\fine a new \
function:
> W1(x1,x2) =3D Z(x1, x2, y1)
> and use your favorite minimization technique. Similarly for
y2.
> - Randy
--
[1;32m Origin:[0m[1;33m
j.b3.bc[Degre
e]T[0m[1m [0m
===
Subject: Re: Question about Surreal Numbers
> Timothy Murphy says...
...
>Because everything is de\fined at once by a single recursive
de\finition,
>starting with nothing but the empty set: a number
>
> x = < L | R >
>
>is de\fined by two sets of numbers L,R with l < r for all l in
L, r in
R.
...
> That is cute, but I dont think you can really get away
from equivalence
> classes. The problem is that this de\finition of number
doesnt have the
> property that x <= y and y <= x --> x=y.
Well, acually there is, without equivalence classes, but the
de\finition
was incomplete. Lets have
x = { Lx | Rx } and y = { Ly | Ry }.
De\finition:
x >= y iff (no x_R in R_x <= y and x <= no y_L in Ly).
x <= y iff y >= x.
x = y iff (x >= y and y <= x).
And the numbers are those x for which:
every x in Lx <= every x in Rx
(the others are games, and for those the ordering relations
do not hold).
This de\fines the basis, although the numbers are not yet
labelled.
Addition, negation and multiplication can be de\fined on this
basis (the
de\finitions are again recursive). For instance, -x is \
de\fined
approximately as { - Rx | - Lx }. And the \first label is
given: 0 = { | }.
0 >= 0 is vacuously true. Next we \find 1 = { 0 | }, and so we
can go on.
Finally it can be shown that the numbers form a \field.
And also you will \find that numbers have different
representations:
1 = { 0 | } = { 0 | 2 } (== { 0 | { 0 | }} ) ...
and so there are equivalence classes, but they are not needed
for the
de\finitions. (And, yes, it looks a bit like a two-sided \
Peano.)
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: swjpam
format=ßowed;
fyi,
The Southwest Journal of Pure and Applied Mathematics
(swjpam) no longer
exists due to budgetary contraints.
===
Subject: Re: swjpam
Discussion, linux)
> fyi,
> The Southwest Journal of Pure and Applied Mathematics
(swjpam) no longer
> exists due to budgetary contraints.
I will never doubt the hammer again. Golly.
--
Conservative, n:
A statesman who is enamored of existing evils, as
distinguished
from the Liberal who wishes to replace them with others.
-- Ambrose Bierce
===
Subject: Re: swjpam
posting-account=UtgH7gwAAACpBhTelVPOXNP7RAfbtQrK
> fyi,
> The Southwest Journal of Pure and Applied Mathematics
(swjpam) no
longer
> exists due to budgetary contraints.
Is that just the excuse? Is the real reason editorial
incompetence?
Is this the \first blow of The Hammer?
===
Subject: do you have any smart way of \finding which number is
bigger ?
Using the fatest way:
compare:
0.9^10 vs. 2*(0.9^19)+0.9^20
how long does it take you to \figure out which number is \
larger?
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
lucy escribi.97:
> Using the fatest way:
> compare:
> 0.9^10 vs. 2*(0.9^19)+0.9^20
> how long does it take you to \figure out which number is
larger?
2*(0.9^19)+0.9^20 = 0.9^10(2*0.9^9 + 0.9^10) =
= 0.9^10(20*9^9 + 9^10)/10^10 = 0.9^10* 9^9*29/10^10
But 9^2 = 81 > 80, then 9^8 > 8^4*10^4 = 4096*10^4
==> 9^9 > 36*10^7 ==> 29*9^9 > 36*29*10^7 = 1044*10^7 > 10^10
--
Ignacio Larrosa Ca.96estro
A Coru.96a (Espa.96a)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
posting-account=Sny74g0AAADy66iGh6ZMdSlIFta_KAXh
Err, the other thing you need to notice along this line is
the 2*
and the addition adding up to 5x
Of course
0.9^20 < 0.9^10
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
posting-account=Sny74g0AAADy66iGh6ZMdSlIFta_KAXh
Err, the other thing you need to notice along this line is
the 2*
and the addition adding up to over 5x
Of course
0.9^20 < 0.9^10
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
posting-account=Sny74g0AAADy66iGh6ZMdSlIFta_KAXh
A: 0.9^10
B: 2*(0.9^19)+0.9^20
Notice both pieces of B are positive. b1 > 0 b2>0
So if I can see one side of + larger than A
then B > A
0.9^20 > 0.9^10
20 > 10
ergo B > A
5 seconds
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
lucy,
Heres a way that doesnt use much explicit \
calculation. (It
admittedly
uses the fact that e < 2.9, which can easily be derived
analytically,
anyway).
The Taylor series for log about 1 is:
log(1+x) = x - (1/2)x^2 + (1/3)x^3 - ...
Setting x = 1/9, we have:
log(10/9)
= log(1 + 1/9)
= (1/9) - (1/2)(1/9)^2 + (1/3)(1/9)^3 - ...
< 1/9
9 * log (10/9) < 1
9 log 10 - 9 log 9 < 1
Adding log 10,
10 log 10 - 9 log 9 < 1 + log 10 = log (e * 10) < log (29)
[Here is where I invoke e < 2.9.]
Subtracting log 9,
10 log 10 - 10 log 9 < log 29 - log 9
10 log (10/9) < log (29/9) = log (2 * (10/9) + 1)
Exponentiating,
(10/9)^10 < 2*(10/9) + 1
Multiplying both sides by (9/10)^20
(9/10)^10 < 2*(9/10)^19 + (9/10)^20
I suspect there is a much more elegant way. Maybe something
with the
expression 10 log 10 - 9 log 9 < log (29)?
Travis
> Using the fatest way:
> compare:
> 0.9^10 vs. 2*(0.9^19)+0.9^20
> how long does it take you to \figure out which number is
larger?
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
> Using the fatest way:
> compare:
> 0.9^10 vs. 2*(0.9^19)+0.9^20
> how long does it take you to \figure out which number is
larger?
I dont know if its smart or fastest, but you \
can factor.
0.9^10 >?< 2 * (0.9^19) + 0.9^20
0.9^10 >?< 2 * (0.9^20)/0.9 + 0.9^20
0.9^10 >?< 0.9^20 * (2/0.9 + 1)
0.9^10 / 0.9^20 >?< 2/0.9 + 1
0.9^-10 >?< 2.2222... + 1
2.8679... < 3.2222...
--
john
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
ETAtAhUAvgUxhHwS5c+oabk25UmVuHI06JUCFAza+
gLCc85dGRk3KQeD5aQy6jyx
0.9^10 ? 2*(0.9^19)+0.9^20
1 ? 2^(0.9^9) + 0.9^10
10^10 ? 20*9^9 + 9^10 = 29*9^9
9^9 = 729^3 > 720^2*700 = 518400*700 > 3.5e8, and 3.5*29 >100.
Therefore ? is <.
--OL
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
> 0.9^10 ? 2*(0.9^19)+0.9^20
> 1 ? 2^(0.9^9) + 0.9^10
> 10^10 ? 20*9^9 + 9^10 = 29*9^9
I followed you up to this point; you are now comparing
10^10 with 29 * 9^9
I dont understand the next line.
> 9^9 = 729^3 > 720^2*700 = 518400*700 > 3.5e8, and 3.5*29
>100.
> Therefore ? is <.
--
john
===
Subject: Re: do you have any smart way of \finding which number
is bigger ?
posting-account=qrPIWAwAAABKr36mTyR-AQd_YQJSbfcG
.9^10 = 0.3486784401
2*(0.9^19) + 0.9^20 = 0.39174699812516770581
The second one is larger
time to do the problem -- (2 seconds for cut and paste maybe?)
===
Subject: Re: re:PROOF that 0.99999... = 1
> heres a much simpler proof:
> statement: .9999999...=1
> since 9x=10x-x,
> 9=9
> 9=9.9999999...-.9999999...
> 9(1)=10(.9999999...)-.9999999
>> 9(1) =/= 9(.999...)
>Huh? Nowhere in this proof does he assume that 9(1) =
9(.999...). He
>assumes 9(1) = 9 (going from the second to last line that
you quoted, to
the
>last line).
>One reason this proof is de\ficient is because of the
assumption that
>10(.9999999...) = 9.9999999... (which is true, but needs to
be proven).
>--Mark
But he assumes .999... = 1 in his equation before it is
proven.
Smarts 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: re:PROOF that 0.99999... = 1
>> heres a much simpler proof:
>> statement: .9999999...=1
>> since 9x=10x-x,
> 9=9
>> 9=9.9999999...-.9999999...
>> 9(1)=10(.9999999...)-.9999999
> 9(1) =/= 9(.999...)
>>Huh? Nowhere in this proof does he assume that 9(1) =
9(.999...). He
>>assumes 9(1) = 9 (going from the second to last line that
you quoted, to
>>the
>>last line).
>>One reason this proof is de\ficient is because of the
assumption that
>>10(.9999999...) = 9.9999999... (which is true, but needs to
be proven).
>>--Mark
> But he assumes .999... = 1 in his equation before it is
proven.
> Smarts Alt. Physics News Group
>
http://pub39.bravenet.com/forum/show.php?usernum=3320272813&
cpv=1
> S. Enterprize (Science Journal)
> http://smart1234.s-enterprize.com/
jesus christ!
do you know anything about mathematical
induction??????????????
let x_n = 9*sum((1/10)^k,k=0..n) = 9*(1 + 1/10 + 1/100 + ..
1/10^n) =
9*(1.11111111...) = 9.999999..
then |10 - x_n| = |10 - 9*sum((1/10^k,k=0..n))| = |10 -
((1/10)^(k+1) -
1)/(1 - 1/10))|
= |1/10^n| = 1/10^n < e for all n >= N > -log(e)
that means, the difference between the in\finitely repeating
decimal with
period one is the same as 10, i.e. 9.9999999...... = 10
(ofcourse, this work
for any number, not just 9)
if you dont believe that x_n = 9.9999999999999999999 then
thats your fault,
you need to learn some simple math.... just try to \find me a
number sticktly
between .999999999999..... and 1!
you can do this for all x if you want...
x = [x] + {x} = ßoor(x) + sum((ßoor((n-x)*10^k) mod 10)/10^k)
if x is terminating or repeating in its tail, then the sum
has a simple
solution and its easy to calculate the answer.
if you put x = 1, the {x} = 0
x = .99999......
then sum is just over 9/10^k which is easily to compute
again, the only thing that you can have any sorta problem
with is how
.9999999999 could be reprsented by the sum, but that is your
problem... as
any halfwit knows that.
===
Subject: Re: PROOF that 0.99999... = 1
> jesus christ!
> do you know anything about mathematical
induction??????????????
Enterprise does not even know what end comes out of. He is a
total
mathematical incompetent. He makes JSH look intelligent by
comparison.
Bob Kolker
===
Subject: Re: A Quantum Poem for Xmas