³ ³ mm-258 === Subject: New Porblem I need help with I got some help on some of my algebra. we got stuck on this problem. the assignment says to do this on a calculator. but we where going to do it without the calculator. the instructor says write the answer in scientific notation. (3.5 x 10^5)(4.3 x 10^-6)/3.4. x.10^-8 we came up with 3.5 * 4.3 3.4/25.050 is what we can up with divide the problem by, and we can up with 4.1117 x 10^7 as the answer. but the textbook show 4.426 x 10^7 as the correct answer does this make sense? I can't make sense of it. can you? M. REVELS mlrisok@sbcglobal.net === Subject: Re: New Porblem I need help with > I got some help on some of my algebra. we got stuck on this problem. > the assignment says to do this on a calculator. but we where going to do it > without the calculator. the instructor says write the answer in scientific > notation. > (3.5 x 10^5)(4.3 x 10^-6)/3.4. x.10^-8 > we came up with 3.5 * 4.3 > 3.4/24.050 at we can up with divide the problem by, and we can up with Makes little sense, can't follow what you're doing. Your work not shown. > 4.1117 x 10^7 as the answer. > but the textbook show > 4.426 x 10^7 as the correct answer > does this make sense? I can't make sense of it. can you? Jump on it; 3.5/3.4 = 1 almost, thus answer close to 4.3 * 10^7 What more exactly? 3.5/3.4 = 1.03 almost as .03 * 3.4 = .1 almost 4.1 * 1.03 = 4.3 + .123 = 4.423 round to nearest tenth 4.4. Ans: 4.4 * 10^7 === Subject: Re: New Porblem I need help with Hi Newsgroup; doing it question. I will let you know how I am doing. I think I got the answer I again newsgroup. -- M. REVELS mlrisok@sbcglobal.net > I got some help on some of my algebra. we got stuck on this problem. > the assignment says to do this on a calculator. but we where going to do it > without the calculator. the instructor says write the answer in scientific > notation. > (3.5 x 10^5)(4.3 x 10^-6)/3.4. x.10^-8 > we came up with 3.5 * 4.3 > 3.4/24.050 at we can up with divide the problem by, and we can up with > Makes little sense, can't follow what you're doing. > Your work not shown. > 4.1117 x 10^7 as the answer. > but the textbook show > 4.426 x 10^7 as the correct answer > does this make sense? I can't make sense of it. can you? > Jump on it; 3.5/3.4 = 1 almost, thus answer close to > 4.3 * 10^7 > What more exactly? > 3.5/3.4 = 1.03 almost as .03 * 3.4 = .1 almost > 4.1 * 1.03 = 4.3 + .123 = 4.423 round to nearest tenth 4.4. Ans: > 4.4 * 10^7 === Subject: Re: New Porblem I need help with >(3.5 x 10^5)(4.3 x 10^-6)/3.4. x.10^-8 >up with >4.1117 x 10^7 as the answer. >but the textbook show >4.426 x 10^7 as the correct answer Not bad, nice result except that since you were given no more than two siginificant figures in the factors main numbers, you should keep only two figures in the answer; better to indicate 4.4 x 10^7 If you really want to stretch it, you might say 4.42 or 4.43, but 4.4 would be best. G C === Subject: Group theory If you have 2 elements,p and q, in the finite group G, and their orders are a and b respectively. Is it true that the order of G is the LCM, the least common multiple of p and q? === Subject: Re: Group theory Adjunct Assistant Professor at the University of Montana. >If you have 2 elements,p and q, in the finite group G, and their >orders are a and b respectively. Is it true that the order of G is >the LCM, the least common multiple of p and q? You mean a and b, presumably. No. Say G = Z/4Z + Z/8Z, a group of order 32; take p the generator of the cyclic group of order 4, and take q to be its inverse. Both are of order 4, the lcm of the orders is 4, but G is of order 32. It's not even true when G is generated by p and q. Take the dihedral group of order 8, G = If you have 2 elements,p and q, in the finite group G, and their > orders are a and b respectively. Is it true that the order of G is > the LCM, the least common multiple of p and q? === Subject: Re: Group theory >If you have 2 elements,p and q, in the finite group G, and their >orders are a and b respectively. Is it true that the order of G is >the LCM, the least common multiple of p and q? Can you construct a counter-example? === Subject: Re: James Harris - Challenge problem > James, > > Since you are busy revolutionalizing mathematics, I understand if you > don't > have time to tackle these. But, if you would like to demonstrate that > you > have any real experience with rings, then these should be fairly easy, > and > might buy you some credibility with the newsgroup. They vary in > difficulty, > but are all elementary abstract algebra. Feel free to use any theorems > that > you know or would like to look up, and do only those that you care to. > > I'm not a mathematician. I'm a discoverer who has a major discovery > which mathematicians should acknowledge. > > Like notice what my blog is called: > > http://mathforprofit.blogspot.com/ > > Now as for any test problems for credibility, who needs credibility? > > Isn't proof supposed to matter in mathematics? > > Don't any of you realize that you've been learning a *democratic* > process, where you demonstrate membership in a group by learning > various abstruse things, which is sort of like a rite of passage. > > It's like hazing where you learn how to repeat things by rote or face > consequences because it shows your dedication to the group. > > But I'm not a mathematician. I have no dedication to your group. > > I'm an outsider with a proof. > > So your *democratic* attacks will not work. Your attempts at pulling > me into social situations dependent on my need to belong will not > work. I don't want to belong in math society. > > I don't need to belong. > > I have a proof. > > Now then, if you doubt that what I have is a proof, try and find an > error in it. > > That's how it works kids. You see, no matter how much effort you put > into belonging in the math world, it never changes the fact that a > proof stands outside of social rules, acceptance or expectations. > > That's why if you think that it really matters whether or not I get > acceptance as a person into your group then much of your past and > current efforts will be to no avail, as the math proof I've found will > destroy your society without ever affecting the proof itself. > > That is, your society will destroy itself trying to change a proof. > > > James Harris > http://mathforprofit.blogspot.com/ > If you want to appear credible, you will answer all objections with > counterarguments without personal attacks. > David Moran > I'll do what's necessary to force mathematicians to do their jobs!!! > And make no mistake, mathematicians are giving me the keys to their > world, and these undergrads had better realize that it doesn't matter > if it takes a few months, or even a couple of more years, as by the > time they can get *anywhere* in the math world, I'll have more power > than they can imagine. > The people who are refusing to acknowledge the truth are wrecking the > society students are trying to become a part of by destroying its > future. > Live in the fantasy world now kids, but time is not on your side, as > mathematical truth will assert itself, and then your *social* world > will crumble to dust. > James Harris Then why haven't I objected to anything my math professors have taught me? David Moran === Subject: math olympiads by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hA90Rs116627; Hi guys!!! Is someone have some training materials for math olympiads for high school olympiads(i'm studying at university). I'll be grateful for you help!!! === Subject: Re: math olympiads jane, The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics It's a dover book, so it's cheap. http://store.yahoo.com/doverpublications/0486277097.html Justin Van Winkle > Hi guys!!! > Is someone have some training materials for math olympiads for high > school olympiads(i'm studying at university). I'll be grateful for you > help!!! === Subject: Re: math olympiads > Is someone have some training materials for math olympiads for high > school olympiads(i'm studying at university). I'll be grateful for you I would recomend: problems from past olympiads (with solutions), problems from past national competitions (Russian, in your case?), and problems from the William Lowell Putnam competition. The last competition is college-level, so some problems assume knowledge beyond that of what you need for the IMO, but those problems are generally easy to recognize (they usually use derivatives or integrals in the problem statement). Many IMOs and Putnams should be readily available online (trying searching on book of older IMO problems, but I have absolutely no idea who published it -- it's been a long time :-) hth meeroh -- If this message helped you, consider buying an item from my wish list: I was wondering if officemax, staples, etc sells paper (online?) that has > extra plastic layers on where the 3 holes of the paper? I'm trying to keep > my math notebook folder neat but when I use it everyday and the paper keep > tearing off. The side pockets aren't enough for it. There's reinforcements for note book holes. I've several decades old boxes of those little gummed annuli, However in our pervers hyper-commercial society, are such simple fixes still availible? === Subject: Re: OT(or not...) > I was wondering if officemax, staples, etc sells paper (online?) that has > extra plastic layers on where the 3 holes of the paper? I'm trying to keep > my math notebook folder neat but when I use it everyday and the paper keep > tearing off. The side pockets aren't enough for it. > There's reinforcements for note book holes. > I've several decades old boxes of those little gummed annuli, > However in our pervers hyper-commercial society, > are such simple fixes still availible? Yes they are. Proving once again the value of free markets. In fact, they now come on sheets, pre-gummed (like postage stamps), so you don't have to wet (dare I say lick?) them yourself. This is a Good Thing. Jon Miller === Subject: JSH Challenge Problem James, I challenge you to prove the following. If N and H are subgroups of a group G, prove that N intersect H is a subgroup of G. If you can prove ANYTHING in algebra, you can prove this. If you can't prove this, you aren't competent enough to claim anything. Hint: The proof is shorter than one long sentance. Hint2: The following is not a valid proof: The intersection SHOULD be a subgroup but it is FORCED out of the group, showing an error in the definition of a group. Justin Van Winkle === Subject: Nice Integration Trick Hi I was surfing around and hit upon the following web page http://www.calculus-help.com/probs2001/4problem21.html The solution for the first problem on this page has two versions - a very long winded one and a great looking shortcut. My problem is that I have no idea what the name of this technique is. Can anyone help? Mike === Subject: Re: Nice Integration Trick > I was surfing around and hit upon the following web page > http://www.calculus-help.com/probs2001/4problem21.html > The solution for the first problem on this page has two versions - a > very long winded one and a great looking shortcut. My problem is that > I have no idea what the name of this technique is. Can anyone help? I presume you're asking about the technique in the shortcut. There are two mistakes. One of them can be very confusing: Using f to name two _different_ things. To clear this mess up, let g(t) denote t^3 -2t + 4. Then everywhere in the shortcut, except on the left side of the second line, replace f by g. The other mistake is just a simple typo: On the right side of the first line, the first term should now be g(b(x)) b'(x), rather than g(b(x)) b(x). HTH David === Subject: What exactly IS a homeomorphism? Hello again, I've come to what seems a fundamental problem in my Topology class: I don't actually understand what a homeomorphism between two spaces really means. I see the whole continuous and bijective parts but... I'm at a loss. Identification spaces brought out this glaring issue with my studies. For example, letting X = {(x,y) in R^2 : y = 0 or y = 1} and defining the identifications ~1 and ~2 such that (x,y) ~1 (u,v) if x = u < 0 or if x = u AND y = v. (x,y) ~2 (u,v) if x = u =< 0 or if x = u AND y = v. Then the spaces X/~1 and X/~2 are not homeomorphic and only one is homeomorphic to a subset of R^2. For the life of me I can't understand why or how. I'm also having trouble understanding what open sets in these spaces would be like, would it be something like (( -e, 0), (e, 0)) U ((0, 1), (e, 1)) where I've defined 2 intervals (between to points in R^2)? Or something else? Ben Scott === Subject: Re: What exactly IS a homeomorphism? > Hello again, > I've come to what seems a fundamental problem in my Topology class: I don't > actually understand what a homeomorphism between two spaces really means. I > see the whole continuous and bijective parts but... I'm at a loss. > Identification spaces brought out this glaring issue with my studies. For > example, letting X = {(x,y) in R^2 : y = 0 or y = 1} and defining the > identifications ~1 and ~2 such that > (x,y) ~1 (u,v) if x = u < 0 or if x = u AND y = v. > (x,y) ~2 (u,v) if x = u =< 0 or if x = u AND y = v. > Then the spaces X/~1 and X/~2 are not homeomorphic and only one is > homeomorphic to a subset of R^2. For the life of me I can't understand why > or how. I'm also having trouble understanding what open sets in these spaces > would be like, would it be something like (( -e, 0), (e, 0)) U ((0, 1), (e, > 1)) where I've defined 2 intervals (between to points in R^2)? Or something > else? > Ben Scott Brian has given you a good answer so I'll try to nudge your intuition a little. Visualize the two spaces: A is the x-axis and the closed half line (x, 1), x >= 0. B is the x-axis and the open half line (x, 1), x > 0. I've already used two homeomorphisms; the topologies of A and B are the usual ones. A is homeomorphic to X/~1; B is homeomorphic to X/~2. Do A and B have different topological properties? What if you remove Otherwise, take Brian's hint about Hausdorff.) Do you see a copy of A in B? Of B in A? -- Paul Sperry Columbia, SC (USA) === Subject: Re: What exactly IS a homeomorphism? >I've come to what seems a fundamental problem in my Topology class: I don't >actually understand what a homeomorphism between two spaces really means. I >see the whole continuous and bijective parts but... I'm at a loss. Have you had an abstract algebra course? If so, you can think of a homeomorphism between topological spaces as the topological analogue of an isomorphism between groups, rings, or fields. To say that there's a homeomorphism between two spaces is to say that they have exactly the same topological structure; only the 'names' of the points are different, and the map tells you how the points in one space correspond to those in the other. In particular, two spaces that are homeomorphic must have exactly the same topological properties. >Identification spaces brought out this glaring issue with my studies. For >example, letting X = {(x,y) in R^2 : y = 0 or y = 1} and defining the >identifications ~1 and ~2 such that >(x,y) ~1 (u,v) if x = u < 0 or if x = u AND y = v. >(x,y) ~2 (u,v) if x = u =< 0 or if x = u AND y = v. >Then the spaces X/~1 and X/~2 are not homeomorphic and only one is >homeomorphic to a subset of R^2. For the life of me I can't understand why >or how. I'm also having trouble understanding what open sets in these spaces >would be like, would it be something like (( -e, 0), (e, 0)) U ((0, 1), (e, >1)) where I've defined 2 intervals (between to points in R^2)? Or something >else? First, what are the points of X/~1 and X/~2? They're the equivalence classes of ~1 and ~2, respectively. Thus, X/~1 has the following points: all singleton sets {(x,0)} and {(x,1)} with x >= 0, and all doubleton sets {(x,0), (x,1)} with x < 0. X/~2 has the following points: all singleton sets {(x,0)} and {(x,1)} with x > 0, and all doubleton sets {(x,0), (x,1)} with x <= 0. In other words, the only difference between them comes at x = 0: in X/~1 the points (0,0) and (0,1) are *not* identified, so that X/~1 has {(0,0)} and {(0,1)} as distinct points, while in X/~2 they *are* identified, so that X/~2 has a single point {(0,0), (0,1)} instead. Now, what do neighborhoods of these points look like? Start with the easiest ones, the points {(x,0)} and {(x,1)} with x > 0, which exist in both spaces. Let e be any positive real number less than x; I claim that the set of points {(u,0)} with such nbhds is a base at {(x,0)} in both X/~1 and X/~2. (You should be able to use the definition of the quotient topology to see why this is true.) Similarly, the set of points {(u,1)} with such nbhds is a base at {(x,1)} in both X/~1 and X/~2. Similarly, {(x,0), (x,1)} is a point of each space for each x < 0. This time you can get a nbhd of {(x,0), (x,1)} by choosing a positive real number e < |x| and forming the set of all points {(u,0), (u,1)} with x-e < u < x+e, and the collection of all such sets is a base at {(x,0), (x,1)} in both X/~1 and X/~2. (Here again you should be able to check this by using the definition of the quotient topology.) Things get more interesting when we look at the points {(0,0)} and {(0,1)} in X/~1 and the point {(0,0), (0,1)} in X/~2. I won't tell you what their nbhds are this time, but I'll give you a couple of pointers. (1) One of X/~1 and X/~2 is homeomorphic to the subset of R^2 consisting of all points (x,y) such that x <= 0, or x > 0 and y = x, or x > 0 and y = -x. (2) The other of X/~1 and X/~2 isn't even Hausdorff (T_2); which two points don't have disjoint open nbhds? Brian === Subject: Newsgroup survey: Math and personality assessment It seems to me that there have been debates over math concepts I thought basic, so here's a quick survey: 1. Before I mentioned it, had you ever heard of the distributive property? 2. In your experience, is math quirky? 3. Do you think that mathematics is an extremely difficult discipline that only experts are really good at handling? 4. What is the distributive property? 5. Is a math proof perfect? 6. Do you consider yourself to be a reasonable person? 7. If a mathematical argument is explained to you in detail, using basic algebra, if it's correct, would you admit that, even to a hostile crowd, like even if many posters on sci.math would call you names and insult you for admitting it? James Harris http://mathforprofit.blogspot.com/ === Subject: Re: Newsgroup survey: Math and personality assessment > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: > 1. Before I mentioned it, had you ever heard of the distributive > property? Yes > 2. In your experience, is math quirky? No. On the other hand, I have run across a few counterintuitive results. > 3. Do you think that mathematics is an extremely difficult discipline > that only experts are really good at handling? Experience would suggest most people consider mathematics difficult. Since any reasonable operational definition (a definition that can actually be used) of an expert in mathematics is someone who is good at handling mathematics, it is tautological that only experts are good at handling mathematics. On the other hand, one does not need a formal education in mathematics to be good at handling mathematics. (Tangential comment: One can no more communicate mathematics to mathematicians without using the language of mathematics than one can communicate philosophy to a French speaker without speaking French.) > 4. What is the distributive property? a(b+c) = ab + ac (Tangential comment. It follows that if a divides c and a divides (b+c) then a divides b.) > 5. Is a math proof perfect? A fairly commonly held view is that a proof is perfect by definition. However, this is not an operational definition. Operationally, we can only talk about a proof that is agreed to be valid (if we insist that a proof must be perfect by definition, then we talk about a proposed proof that is agreed to be (or represent) an actual proof). > 6. Do you consider yourself to be a reasonable person? Yes. > 7. If a mathematical argument is explained to you in detail, using > basic algebra, if it's correct, would you admit that, even to a > hostile crowd, like even if many posters on sci.math would call you > names and insult you for admitting it? I am not immune to social pressure, but if I thought a mathematical argument was valid, I would certainly admit this on sci.math. However, I have a lot of respect for many of the posters on sci.math. If they insisted I was wrong, I would check the argument carefully. I would ask them to explain exactly where they thought the error was in the argument, and if I did not understand, ask again (fortunately, many of the posters on sci.math are very patient, especially with anyone who appears to be making an honest effort to learn). I would never insult them or threaten them with legal action if they disagreed with me, even if I thought them mistaken. Now that I have answered your survey, maybe you could answer a short quiz. What is the constant term of the following three functions? U(x) = sqrt(x^2 + x)/sqrt(x+7) + 7/sqrt(x+7) V(x) = sqrt(x^2 + x)/7 + 7/7 W(x) = sqrt(x^2 +x)/(x^2 +2x +7) + 7/(x^2 +2x +7) (hint: The constant term of b(x) is b(0) ) - William Hughes === Subject: Re: Newsgroup survey: Math and personality assessment > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: > 1. Before I mentioned it, had you ever heard of the distributive > property? Yup. > 2. In your experience, is math quirky? Quirky as in unexpected twists and turns? Nope, nothing's quirky when you understand it. Quirky as in having a characteristic peculiarity of habit or structure? Yup, the peculiarity is called CONSISTENCY. > 3. Do you think that mathematics is an extremely difficult discipline > that only experts are really good at handling? Nope. Math comes in all levels of difficulty, some of it I can handle, some of it I can't. > 4. What is the distributive property? Dis goes over here an dat goes over dere. > 5. Is a math proof perfect? How do you grade proofs? Aren't they either right or wrong with no middle ground? > 6. Do you consider yourself to be a reasonable person? Yup. But only in reasonable dialog. Name calling, threats, treason and other boorish behaiviour tend to receive response in kind. > 7. If a mathematical argument is explained to you in detail, using > basic algebra, if it's correct, would you admit that, even to a > hostile crowd, like even if many posters on sci.math would call you > names and insult you for admitting it? Only if _I_ understood it to be correct. > James Harris > http://mathforprofit.blogspot.com/ === Subject: Re: Newsgroup survey: Math and personality assessment http://www.crank.net/harris.html http://www.crank.net/harris.html > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: http://www.crank.net/harris.html > 1. Before I mentioned it, had you ever heard of the distributive > property? http://www.crank.net/harris.html > 2. In your experience, is math quirky? http://www.crank.net/harris.html > 3. Do you think that mathematics is an extremely difficult discipline > that only experts are really good at handling? http://www.crank.net/harris.html > 4. What is the distributive property? http://www.crank.net/harris.html > 5. Is a math proof perfect? http://www.crank.net/harris.html > 6. Do you consider yourself to be a reasonable person? http://www.crank.net/harris.html > 7. If a mathematical argument is explained to you in detail, using > basic algebra, if it's correct, would you admit that, even to a > hostile crowd, like even if many posters on sci.math would call you > names and insult you for admitting it? http://www.crank.net/harris.html http://www.crank.net/harris.html > James Harris > http://mathforprofit.blogspot.com/ http://www.crank.net/harris.html === Subject: Re: Newsgroup survey: Math and personality assessment >It seems to me that there have been debates over math concepts I >thought basic, so here's a quick survey: >1. Before I mentioned it, had you ever heard of the distributive >property? Yes, I'd seen (but not understood) it on the sci.math newsgroup >2. In your experience, is math quirky? No, just perhaps not really something I understood >3. Do you think that mathematics is an extremely difficult discipline >that only experts are really good at handling? No, just people who are better at that sort of discipline than I am. I have an (extremely) basic grounding in O Level maths >4. What is the distributive property? No idea >5. Is a math proof perfect? Possibly, if it starts with something that people understand, progresses in steps that people understand, and finishes with a conclusion that people understand. (I do not consider myself 'people' - I do not understand enough what I would call 'higher' math). However, I do understand obfuscation, rudeness, obnoxiousness (spill chicken does not recognise this as a word) and idiocy - all of which you display >6. Do you consider yourself to be a reasonable person? No, I know I'm a reasonable person >7. If a mathematical argument is explained to you in detail, using >basic algebra, if it's correct, would you admit that, even to a >hostile crowd, like even if many posters on sci.math would call you >names and insult you for admitting it? Absolutely - what I do not admit is someone, who admits to a mistake, merely saying 'OOPS' and failing to apologise to your 'silent majority' for calling everyone else in the thread 'liars' 'dog****' and any other perjoratives you used. Hope you enjoyed it. -- Min So where are all the buffaloes? === Subject: Re: Newsgroup survey: Math and personality assessment > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: > 1. Before I mentioned it, had you ever heard of the distributive > property? Yes, I'm sure everyone with a 8th grade education has too > 2. In your experience, is math quirky? There have been a few things in my mathematical training that didn't make sense at first, but once I studied on it more, it became clear. > 3. Do you think that mathematics is an extremely difficult discipline > that only experts are really good at handling? I think everyone is capable of learning mathematics if they are well prepared. > 4. What is the distributive property? a(b+c)=ab+ac > 5. Is a math proof perfect? That question is vague, the logic may be flawed, producing an incorrect proof > 6. Do you consider yourself to be a reasonable person? Yes > 7. If a mathematical argument is explained to you in detail, using > basic algebra, if it's correct, would you admit that, even to a > hostile crowd, like even if many posters on sci.math would call you > names and insult you for admitting it? I don't think they'd call me names or insult me if I was willing to understand where I went wrong. > James Harris > http://mathforprofit.blogspot.com/ === Subject: Re: Newsgroup survey: Math and personality assessment >It seems to me that there have been debates over math concepts I >thought basic, so here's a quick survey: >1. Before I mentioned it, had you ever heard of the distributive >property? Never. >2. In your experience, is math quirky? Don't have any experience with math, so I couldn't say. >3. Do you think that mathematics is an extremely difficult discipline >that only experts are really good at handling? Not sure. >4. What is the distributive property? Dunno. >5. Is a math proof perfect? Never saw one, couldn't say. >6. Do you consider yourself to be a reasonable person? Yes. >7. If a mathematical argument is explained to you in detail, using >basic algebra, if it's correct, would you admit that, even to a >hostile crowd, like even if many posters on sci.math would call you >names and insult you for admitting it? Absolutely not - I'll go along with the crowd on _anything_, whether the crowd is right or not, if I fear they'll call me names and insult me if I don't go along. Why, that's why I've agreed with _you_ all these years - I know you'll call me a piece of ing dog if I don't. You know, your hypocrisy is just sickening. >James Harris >http://mathforprofit.blogspot.com/ === Subject: Re: Newsgroup survey: Math and personality assessment ----- Original Message ----- === Subject: Newsgroup survey: Math and personality assessment > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: > 1. Before I mentioned it, had you ever heard of the distributive > property? Can you prove basic things in algebra? Do you KNOW basic things about algebra? I submit that you do not. I guess I will expand on this a bit more. Yes, everyone has heard of the distributive property who has even the cheesiest mathematics background. Despite what you may think, you are not teaching anyone anything here. In fact, I may be slightly dumber for having read your posts. > 2. In your experience, is math quirky? This question doesn't sit well with me. Quirky isn't a word that has a definition that might be applied to mathematics and make sense. Usually, in the usage that I've witnessed, quirky means something like wierd. So in my experience, math can be weird- meaning that it can be counter-intuitive. > 3. Do you think that mathematics is an extremely difficult discipline > that only experts are really good at handling? By definition, only experts are 'really good' at anything, since if you are really good at something then you are an 'expert'. Or, perhaps, expert means knowledgable. Then again, I contend that yes, you must be very knowledgable to be really good at math. Read Theatetus for more on this. > 4. What is the distributive property? Give an example of something that doesn't exibit the distributive property, James. I'll even give you a hint, the VAST majority of rings have the distributive property. (IE both right and left distributive properties)... wait, you did know that there are two distributive properties in the ring axioms, right? Oh, I forgot, you aren't aware of basic mathematical facts. You see, there are these rings that don't commute. Do you know what commute formal symbols that commute then the order they are 'multiplied' doesn't matter. Do you know what I mean when I say 'multiplied'? You see, James, the product in a ring doesn't have to be multiplication like you learned in 3rd grade. It can be anything, so long as it satisfies the ring axioms. Do you know what those are? Had you heard of any of this before I told you? > 5. Is a math proof perfect? This is not a well defined question. One might say that a correct math proof is perfect. However, one might also compare two correct proofs and say that one is superior to the other, which contradicts the idea that they are each perfect. I'll just paraphrase one of my professors, I'm sure James will get a kick out of this: What constitutes a proof is defined by the community of mathematicians. If mathematicians were much smarter, then proofs could be much looser, since much more would be obvious. If mathematicians were a little dumber, then proofs would have to include many more steps. In other words, the criteria for what constitutes a proof are not an absolute. However, in the mathematics James has actually seen, this might not be so true. For example, two column proofs, like you might do in a high school geometry class, are virtually unquestionable (assuming they are logically correct). > 6. Do you consider yourself to be a reasonable person? Every person considers him or herself a reasonable person, especially those who aren't especially reasonable. Depending on what definition of rational you use, one could handily argue that no human is rational, and in fact irrationality is a pre-requisite for life to be successful. A perfectly rational being would then be completely nihilistic in this line of reasoning. See Beyond Good and Evil for more on this. Possibly, by reasonable you mean something else. The real question should be, do you consider most other people reasonable. For example, if you were to consider almost every expert in a field unreasonable, then logically there are only 2 reasonable conclusions you could make. Either a) I'm missing something, or b) the field is corrupt and these people are merely posing as experts. Now, we have what I might copyright as The Sanity Criterion. A sane person would realize that there are millions of very smart people in the world. Even if one were incredibly brilliant, the chances are very low that there are not thousands of equally brilliant people in the world. Finally, a sane person would realize that those thousands of brilliant people would have uncovered this MASSIVE conspiracy already. Finally, one might realize that although one could refer to this collection of people with one word, it is in fact a varied and splintered collection of often disagreeing individuals. These individuals have nothing to gain from said conspiracy, nor any power to enforce it. So to take option b) would not satisfy the sanity criterion. > 7. If a mathematical argument is explained to you in detail, using > basic algebra, if it's correct, would you admit that, even to a > hostile crowd, like even if many posters on sci.math would call you > names and insult you for admitting it? This was difficult to parse, but the gist of it seems to be would you be afraid to say that you think something is true (if you believe it is true) to a hostile audience. I would enjoy doing so. However, basic algebra is what you might learn in 7th grade. Anything with the word 'ring' excluding 'the lord of the' would be considered 'abstract' or 'modern' algebra. 'in detail' would mean that it was logical. and 'correct' would mean that it has an implication to test. No, thank you, Kurt. > James Harris > http://mathforprofit.blogspot.com/ Justin Van Winkle === Subject: Re: Newsgroup survey: Math and personality assessment > It seems to me that there have been debates over math concepts I > thought basic, so here's a quick survey: James is the person who's always whining about social issues in mathematics and accusing mathematicians of caring more about each other's opinions than about the Truth. So why is he also the only person who conducts these ridiculous opinion surveys? Does he *really* think that *this time* he's going to find that the masses are on his side? And why does he care *what* everyone else thinks, if he's so sure he's right? -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock