Search found 17 matches

by nachomancer
Wed Jun 08, 2011 8:57 pm UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

Edit: while on mathoverflow, I also noticed this question , which is relevant to our discussion. I was just about to post this! I was happy to see that people with far more knowledge of logic than me can confirm that my thinking was sound. Here is what Gowers had to say (blatant argument by authori...
by nachomancer
Sun Jun 05, 2011 9:41 pm UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

That doesn't in anyway contradict what I said. Proofs in ZFC + Axiom X are meaningless. I can prove the moon is made of cheese in ZFC + Axiom X. Proofs in ZFC are not meaningless. If the opposite of a given "true" statement can also be "proven", in what sense is any statement me...
by nachomancer
Sat Jun 04, 2011 9:26 pm UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

Things are explained using naive set theory because it's intuitive. These things can also be proven with a consistent set theory. But if we can't prove it with a consistent theory it is meaningless. Saying "if you avoid contradiction you can still get useful results" is ludicrous because ...
by nachomancer
Sat Jun 04, 2011 8:51 am UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

That still doesn't make sense. Your axioms being inconsistent will make them useless. Whether or not I can reach a contradiction in less than n steps doesn't matter. The contradiction exists, and that's all that matters. What you're describing seems to be like saying "It all makes sense as lon...
by nachomancer
Fri Jun 03, 2011 11:21 pm UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

This is relevant. If the system is no longer consistent, your axioms must contain a contradiction and so any derived statement is ultimately meaningless as the opposite could also be "proven". It may be interesting to note that two axioms are contradictory, but other than that, nothing wi...
by nachomancer
Fri Jun 03, 2011 12:45 am UTC
Forum: Mathematics
Topic: Math is a language, not a science?
Replies: 87
Views: 24053

Re: Math is a language, not a science?

Maths is the science of consistent systems. This might be considered a minor quibble (and isn't relevant to the OP's question), but this seems too restrictive to me. If I found that a given axiomatic system was inconsistent, but that, say, the shortest contradiction was of a particular length, this...
by nachomancer
Wed May 11, 2011 6:40 pm UTC
Forum: Mathematics
Topic: Formal mathematical definition of area
Replies: 10
Views: 2264

Re: Formal mathematical definition of area

For most reasonable shapes, the Riemann integral works fine. If you are interested in a more general definition, I would suggest reading up on measure theory. Wikipedia has pretty good articles on both topics.
by nachomancer
Wed May 11, 2011 6:35 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 157757

Re: Math: Fleeting Thoughts

I often wonder about Brouwer's fixed point theorem. I.e "Every continuous function f from a closed disk to itself has at least one fixed point." Say, by means of an analogy we are stirring a cup of coffee. At any two points in time there is some point which has not moved. Do these fixed p...
by nachomancer
Fri Apr 29, 2011 9:26 pm UTC
Forum: Mathematics
Topic: Silly inequality question
Replies: 21
Views: 2735

Re: Silly inequality question

More directly this is just the statement that the "squaring" function is convex.
by nachomancer
Fri Apr 29, 2011 4:24 pm UTC
Forum: Mathematics
Topic: Must a ring have multiplicative identity?
Replies: 8
Views: 2890

Re: Must a ring have multiplicative identity?

If you don't like it, go edit the article. Thats kind of the whole point of wikipedia...
by nachomancer
Fri Apr 29, 2011 6:36 am UTC
Forum: Mathematics
Topic: 6÷2(1+2)=?
Replies: 7
Views: 2106

Re: 6÷2(1+2)=?

Seriously?
by nachomancer
Mon Apr 25, 2011 6:34 pm UTC
Forum: Mathematics
Topic: What is this law/identity/thing called?
Replies: 10
Views: 1868

Re: What is this law/identity/thing called?

That identity is usually included as an axiom in the definition of a vector space. It is actually kind of important on its own, as it expresses the fact that scalar multiplication (of a vector) and field multiplication are compatible. This is also true for modules, which don't always have a basis, s...
by nachomancer
Mon Apr 25, 2011 4:04 pm UTC
Forum: Mathematics
Topic: What is this law/identity/thing called?
Replies: 10
Views: 1868

Re: What is this law/identity/thing called?

You should know that all properties of real number (or fields, more generally) under addition and multiplication follows from associativity, commutativity and distribution of multiplication over addition. Therefore, any identity of real numbers you see is just those operations in disguise.
by nachomancer
Wed Apr 20, 2011 9:55 am UTC
Forum: Mathematics
Topic: Getting my undergrad in math. How about you?
Replies: 51
Views: 8249

Re: Getting my undergrad in math. How about you?

Age: 18
Education: Finishing junior year of math major
Currently: Working on summer project in character/representation theory. So far my matrices have been rather small though...
by nachomancer
Tue Apr 19, 2011 2:16 am UTC
Forum: Mathematics
Topic: If you learned statistics would you never buy insurance?
Replies: 92
Views: 10734

Re: If you learned statistics would you never buy insurance?

Would you rather have a 1% chance to get 2 trillion dollars, or a 100% chance of getting a billion dollars? Even though your expected value is higher in the first case, it is entirely rational for an individual to choose the second. The reason is that the true value of money is not linear. In other ...
by nachomancer
Sat Oct 09, 2010 8:04 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 488326

Re: Favorite math jokes

An infinite number of mathematicians walk into a bar. The first one orders one beer. The second orders two beers. The third orders four beers, and the fourth orders 8 beers. The bartender complains, "If you all keep this up, I'm going to end up owing you a beer" http://en.wikipedia.org/wik...
by nachomancer
Wed Apr 14, 2010 5:43 am UTC
Forum: Mathematics
Topic: Pythagorean Triples
Replies: 1
Views: 703

Pythagorean Triples

Hello all, This being my first post, I figure I should say some quick words about myself. I'm a high school student currently finishing up with Calc 3. I've done a fair amount of reading/problem solving on my own, and certainly plan on doing lots of math in college. I was doing some thinking about n...

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