Search found 42 matches

by Pietro
Fri Aug 21, 2009 8:48 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0626: "Newton and Leibniz"
Replies: 213
Views: 58613

Re: "Newton and Leibniz" Discussion

I can already see what the commenters at XKCD sucks are going to say about this. "What? Me no get the joke" FIRST-YEAR CALCULUS IS EASY. GET OVER YOURSELF. So it's not a reference to graduate school math. Who cares? Um, if you had read for context, you would have seen that my point was di...
by Pietro
Fri Aug 21, 2009 6:07 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0626: "Newton and Leibniz"
Replies: 213
Views: 58613

Re: "Newton and Leibniz" Discussion

And what's even better is all the people not catching the CSI: Miami reference. I thought that was a meme of the internet by now. Oh, hooray. The internet meme is one-liners with sunglasses. So the joke is Newton making a lame one-liner pun with sunglasses. HOORAY. Also the webcomic of romance, sar...
by Pietro
Fri Aug 21, 2009 4:10 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0626: "Newton and Leibniz"
Replies: 213
Views: 58613

Re: "Newton and Leibniz" Discussion

Looks like neoliminal is keeping his dignity.

Also, sweet jesus in heaven. Xkcd "humor" is now bordering on Brightly Wound. RANDALL, GO ON SABBATICAL. GIVE YOURSELF TIME TO GET IDEAS. IF GARY LARSON NEEDED IT, YOU SURE AS HELL AREN'T ABOVE IT.
by Pietro
Wed Aug 19, 2009 3:40 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0625: "Collections"
Replies: 137
Views: 34743

Re: "Collections" Discussion

Have to agree with SirMustapha and Ithaca. This comic is almost as bad as "Haiku Proof". And, as has been increasingly the case, discussion just turns into a pissing contest to see who wins at the topic in the comic. (In this case, who has the most Pratchett books.) Then again, it's not as...
by Pietro
Fri Aug 14, 2009 3:59 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0622: "Haiku Proof"
Replies: 126
Views: 42143

Re: "Haiku Proof" discussion

This comic is painful. Last two weeks have been pretty bad, but this one is particularly awful. It is also a bit sad that the "webcomic of romance, sarcasm, math and language" has so little math. In fact, the whole "xkcd is great at science" hype has been looking pretty silly for...
by Pietro
Thu Jul 30, 2009 3:41 pm UTC
Forum: Mathematics
Topic: Continously adding digits to a number
Replies: 15
Views: 1595

Re: Continously adding digits to a number

notzeb wrote:um... after you stick a 3 onto the end of the number, it isn't of the form 2a5b. "Problem" solved.


Oooh... color me silly.
by Pietro
Thu Jul 30, 2009 7:22 am UTC
Forum: Mathematics
Topic: Continously adding digits to a number
Replies: 15
Views: 1595

Re: Continously adding digits to a number

It remains to prove that there exists r such that (3n+1)10 r −1 isn't a power of three. (Nice use of the big guns, by the way.) The answer to this specific problem can be got by subtracting consecutive terms: [(3n+1)10 r+1 −1] - [(3n+1)10 r −1] = 9(3n+1)10 r So 9 is the biggest power of 3 dividing ...
by Pietro
Thu Jul 30, 2009 7:13 am UTC
Forum: Mathematics
Topic: Continously adding digits to a number
Replies: 15
Views: 1595

Re: Continously adding digits to a number

Good starting observations, and nice proof for n not of the form 2 a 5 b . Unfortunately I couldn't come up with a fix, and ended up with a proof for the general case instead. Here it is: let p be a prime factor of the number 10n+3. Obviously it can't be 2 nor 5. Now put k=p. By Fermat's Little, we ...
by Pietro
Sun Jul 26, 2009 5:20 pm UTC
Forum: Mathematics
Topic: Book Club: Mathematics: Its Contents... discussion
Replies: 50
Views: 5336

Re: Book Club: Mathematics: It's Contents... discussion

Perhaps I'm taking things more slowly than most, since right now I'm a bit swamped with work (thesis writing), but I was somewhat taken aback by the fact that discussion jumped straight into chapter 2, "Analysis". I just finished reading chapter 1, and it sure is interesting! Did you guys ...
by Pietro
Sat Jul 25, 2009 11:02 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 488465

Re: Favorite math jokes

Oh, the thread is too long, I'll just post this joke and hope it isn't a repeat! The sad thing is, if people would read the thread, there wouldn't be a dozen copies and fifty slight variants of each single joke posted. Then the thread would still probably be under 10 pages long, and it would be qui...
by Pietro
Thu Jul 23, 2009 7:14 pm UTC
Forum: Mathematics
Topic: Area of the Primes / Overstimulated
Replies: 6
Views: 956

Re: Area of the Primes / Overstimulated

I haven't checked your MatLab code (I don't really know MatLab), but it is to be expected that the sum increases very slowly. In fact, if p n denotes the n-th prime, it is a theorem that \sum_{i=1}^n \frac{1}{p_i} \ \approx \ \log \log n So it's quite reasonable that, at 50,000, you should see somet...
by Pietro
Sat Jul 18, 2009 6:06 am UTC
Forum: Mathematics
Topic: Graph Theory (Bollobás) Discussion
Replies: 21
Views: 2318

Re: Graph Theory (Bollobás) Discussion

RabidAltruism, I don't mean to be a spoilsport, but perhaps that wasn't the best possible acquisition. First, it's not really by Bollobas, but a collection of survey papers by many authors, edited by Bollobas. Not necessarily a bad thing, but I'm not familiar with any of the other authors' styles, e...
by Pietro
Fri Jul 17, 2009 12:19 pm UTC
Forum: Mathematics
Topic: Graph Theory (Bollobás) Discussion
Replies: 21
Views: 2318

Re: Graph Theory (Bollobás) Discussion

Let me just add a word of encouragement: I've worked through about half that book, and it is an EXCELLENT book. The prose is clear and enlightening, the proofs elegant, and the overall structure very wel thought-out. If anyone else has a fancy for combinatorics, I can recommend pretty much everythin...
by Pietro
Fri Jul 17, 2009 12:16 pm UTC
Forum: Mathematics
Topic: A Happy Prime Problem
Replies: 11
Views: 1885

Re: A Happy Prime Problem

I have no insight into the original problem, but here's a fun one (which I have not been able to solve either). All our integers will be expressed in base 10 (this is arbitrary). Consider the happy function, given by the sum of the squares of the digits: happy(21) = 2²+1¹ = 5 happy(123) = 1²+2²+3² =...
by Pietro
Fri Jul 17, 2009 11:48 am UTC
Forum: Mathematics
Topic: Mathematics: Discovered or Invented?
Replies: 39
Views: 4780

Re: Mathematics: Discovered or Invented?

we didnt set up the rules. [...] we didnt determine that if you take two neutrons, there is twice as many as if we take one. Yes, we did set up those rules, when we (our brains) elected to interpret a section of sensory input as "one neutron", as something separate from everything else. Y...
by Pietro
Fri Jul 17, 2009 9:09 am UTC
Forum: Mathematics
Topic: Mathematics: Discovered or Invented?
Replies: 39
Views: 4780

Re: Mathematics: Discovered or Invented?

I'm going to say some things which have been beaten to death in the philosophy of math. We invented pi for the very simple reason that we invented circles. There are no circles in the real world. We also invented the notion of discreteness which allows us to count things. It is your mind that separa...
by Pietro
Fri Jul 17, 2009 8:59 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

I very much do want to invite comparison of the "validity" of a proof to other properties by which we judge it. What makes validity (as we interpret that word today) so special? What do we even mean by validity? We seem to be talking at cross-purposes. I'm using "validity" of a ...
by Pietro
Thu Jul 16, 2009 11:12 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

I think antonfire was talking about preferences for different kinds of valid proofs, not preferring invalid proofs. That doesn't follow at all from what he was saying. I don't think antonfire advocates invalid proofs. Antonfire is probably every bit as able at mathematics as I am, or more. Neverthe...
by Pietro
Thu Jul 16, 2009 10:42 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

To get back on topic, I just wanted to make clear my original point. I first said that "formal systems are not the holy grail", and t0rajir0u said something that could be read as, "yeah, everyone does math their own way, and formal systems are as good as anything else". (I don't ...
by Pietro
Thu Jul 16, 2009 10:36 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

Standards for the loosest acceptable proof for a*0=0 vary from "it's obvious" to the full axiomatic proof with justifications for each step. I'm not sure if you meant to pick any example and went with "0=0" by accident, but it's not a good one. In fact, "0=0" i...
by Pietro
Thu Jul 16, 2009 7:08 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

Hear, hear. The community standards for what constitutes an acceptable proof are just that; standards. They vary over time like any other set of standards. I sympathize with one possible reading of your post, but maybe there's room for misunderstanding. I don't think you misunderstand anything, jud...
by Pietro
Thu Jul 16, 2009 6:34 am UTC
Forum: Mathematics
Topic: Mathematics: Discovered or Invented?
Replies: 39
Views: 4780

Re: Mathematics: Discovered or Invented?

For many interested laypeople who are not practising mathematicians, mathematics has a sort of mystical aura of awesomeness about it. Things are "deep", "eternal" and whatnot. Though there's nothing necessarily wrong with that, it can negatively affect one's clear thinking about ...
by Pietro
Sat Jul 11, 2009 9:36 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

Continuing with point (1) and the objection that Euclid does not state nor prove the comparability of any pair of natural numbers. One thing the objector claimed was that this was dealt with by the advent of "rigor" a hundred years ago, where people started writing down explicit axiom syst...
by Pietro
Sat Jul 11, 2009 7:58 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

t0rajir0u and skeptical scientist: I'm glad you found my post to be of interest. I agree with both your statements on point (1), and they are important things to keep in mind. Nevertheless, I would like to address more directly the question "do mathematical logic and formal systems provide a gr...
by Pietro
Sat Jul 11, 2009 7:48 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Re: Some points on mathematical logic and "rigor"

Let's tackle point (1). I'll start by reviewing a paradigmatic argument about the "lack of rigor" of earlier mathematicians, presented by forum member Gaydar2000SE's. It is well-known that Euclid's Elements contains a proof that there are an infinite number of primes. Gaydar2000SE contends...
by Pietro
Sat Jul 11, 2009 7:12 am UTC
Forum: Mathematics
Topic: Some points on mathematical logic and "rigor"
Replies: 27
Views: 4333

Some points on mathematical logic and "rigor"

Dear forum, quite recently, there were a couple of threads on "rigor" in mathematics, and the inevitable accompanying discussion of mathematical logic and its perceived achievements. At least one forum member felt that "rigor" is a newcomer to mathematics, originating only "...
by Pietro
Sat Jul 11, 2009 5:03 am UTC
Forum: Mathematics
Topic: Egyptian fractions
Replies: 13
Views: 2550

Re: Egyptian fractions

Open? It was proved in 2003 - http://arxiv.org/PS_cache/math/pdf/0311/0311421v1.pdf. Oh my, so it was. I guess I should have read the Wikipedia page. It's a rather ingenious argument, by the way. The only non-elementary bit of mathematics that goes into the result seems to be the prime number theor...
by Pietro
Fri Jul 10, 2009 10:53 am UTC
Forum: Mathematics
Topic: Egyptian fractions
Replies: 13
Views: 2550

Re: Egyptian fractions

PM 2Ring, it's true, egyptian fractions give rise to some pretty interesting problems, with a decidedly unique taste. Here are a couple: [Fun exercise.] Let q be a rational number between 0 and 1. We call 1/x + 1/y + ... + 1/w a strict egyptian representation of q if x,y,...,w are distinct positive ...
by Pietro
Thu Jul 09, 2009 10:31 am UTC
Forum: Serious Business
Topic: Life: Overrated Coincidence or Spiritual Goal?
Replies: 70
Views: 6347

Re: Life: Overrated Coincidence or Spiritual Goal?

The greatest goal of the human species is to truly know the meaning of everything. Why they are here, how they works, the meaning of life, etc... I'm sorry, when did the human species last vote on its greatest goal? Was it unanimous? Do they have a new vote every time someone is born? And seriously...
by Pietro
Thu Jul 09, 2009 7:55 am UTC
Forum: Mathematics
Topic: Egyptian fractions
Replies: 13
Views: 2550

Re: Egyptian fractions

You can also add any perfect square simply because all of the numbers can be the same. ie, 6+6+6+6+6+6=36 1/6+1/6+1/6+1/6+1/6+1/6=1 You're quite right, but it was the first thing we noticed on this thread! :o) You're also right regarding your egyptian/strictly egyptian question. Indeed, it seems (n...
by Pietro
Tue Jul 07, 2009 10:17 am UTC
Forum: Mathematics
Topic: Egyptian fractions
Replies: 13
Views: 2550

Re: Egyptian fractions

A small observation I just made, which answers the last question: lemmas 1 & 2 can never be used to show that any prime number works. (Look at the conclusions in them.) Nevertheless, some prime numbers work! The smallest of these is 11: 2 + 3 + 6 = 11 1/2 + 1/3 + 1/6 = 1 The plot thickens... Her...
by Pietro
Tue Jul 07, 2009 9:48 am UTC
Forum: Mathematics
Topic: Egyptian fractions
Replies: 13
Views: 2550

Re: Egyptian fractions

This problem is fascinating! I haven't solved it, but here's some partial progress. We'll say that a natural number N works iff there are natural numbers x 1 ,...,x i such that x 1 +...+x i =N and 1/x 1 +...+1/x i =1. The first obvious thing I noticed was that perfect squares always work. You just t...
by Pietro
Sun Jun 21, 2009 10:27 am UTC
Forum: Mathematics
Topic: Greater achievement - Perelman's or Wile's proof?
Replies: 23
Views: 3438

Re: Greater achievement - Perelman's or Wile's proof?

I mean, what if Wiles first proved that elliptic curve thing, forgot how it was called. And then some other person came with 'Yeah, but if fermat's is true, then some elliptic curves aren't modular, didn't some guy 50 years back prove that ALL elliptic curves are?', would they then posthumously awa...
by Pietro
Fri Jun 19, 2009 8:34 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0599: "Apocalypse"
Replies: 158
Views: 56547

Re: "Apocalypse" Discussion

Daniel Kleitman, a combinatorialist at MIT (not a consultant), is famous for having solved more than a handful of problems proposed by Erdos(*), and in the process acquired an Erdos number 1. He also consulted for "Good Will Hunting", which gave him a Bacon number 2 via Minnie Driver. http...
by Pietro
Wed Apr 02, 2008 7:51 am UTC
Forum: Mathematics
Topic: Levels of Infinity (theory)
Replies: 63
Views: 7413

Re: Levels of Infinity (theory)

The standard real numbers are complete, and do not have infinitesimals. I think the term you had in mind was "archimedean" rather than "complete". There is a rather simple proof that something very "like" the real numbers, but with infinitesimals, exists. To wit, let T...
by Pietro
Tue Feb 19, 2008 11:17 pm UTC
Forum: Mathematics
Topic: Pure Maths - putting it all together
Replies: 33
Views: 3533

Re: Pure Maths - putting it all together

Yakk wrote: Neat -- are those equivalencies more interesting than "they are equally true"? Yes; the point is that the equivalence is "much easier" to prove than the theorems themselves, in the sense that very weak logical systems can do it. In particular, logical systems which c...
by Pietro
Tue Feb 19, 2008 5:22 pm UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1911

Re: Realism?

dosboot wrote: It seems to bring into question whether model theory is actually relevant to mathematics. Stepping outside an arbitrary set theory and studying it with model theory seems as relevant as stepping outside model theory and studying it with an arbitrary set theory. Oh yes, model theory i...
by Pietro
Mon Feb 18, 2008 11:20 pm UTC
Forum: Mathematics
Topic: Pure Maths - putting it all together
Replies: 33
Views: 3533

Re: Pure Maths - putting it all together

Robin S wrote: That is why all I am looking for is an outline of how to build up from ZFC to other areas of maths, rather than a way of doing advanced maths in set-theoretic notation. You've said this a couple of times already, in response to people showing how to define standard mathematical struc...
by Pietro
Mon Feb 18, 2008 9:01 am UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1911

Re: Realism?

ErrantBit writes: How do higher-order logics permit theories with no countable model? This isn't so hard to see. How does first-order logic allow for theories without a finite model? Choose a language with at least one function symbol, f, and equality, =, and consider the following theory (in forma...
by Pietro
Mon Feb 18, 2008 8:22 am UTC
Forum: Mathematics
Topic: Pure Maths - putting it all together
Replies: 33
Views: 3533

Re: Pure Maths - putting it all together

Kolmogorov & Fomin is an excellent book, particularly because, when a concept is introduced, they give examples which are interesting in their own right; many of which actually motivated the development of the abstract theory. (Don't you hate it when textbooks give the trivial example first? &qu...

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