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General Discussion => Other Discussions => Math and Science => Topic started by: ruler501 on March 22, 2014, 11:54:33 pm

Title: Interesting Theoretical Math Problems
Post by: ruler501 on March 22, 2014, 11:54:33 pm

What are some really interesting math problems you know of?

One I worked on the other day and neither of my math professors had a quick answer to was: Construct 3 disjoint open sets in R with the same boundary, if it is not possible prove why.

Spoiler For answer:

The intuitive answer that it is not possible because you can't have three disjoint open sets that share a boundary point(this is false at least in R).

The correct proof from this is a proof that in R if a set A is a subset of another closed set B and they share a boundary then the closure of A equals B. With this you can prove that the closure of the first set is equal to both of the other sets. Therefore the other two sets are equal. Two disjoint sets cannot be equal so they cannot exist.
I know this isn't formal, I do have a formal proof, but formatting really doesn't go well on the forums here.

Anyone else have interesting theoretical problems like this?

EDIT: I'm more interested in topics in topology and analysis(recently I've been looking at the cantor like middle-m sets).

Title: Re: Interesting math questions
Post by: willrandship on March 23, 2014, 12:08:52 am

Check these out.

https://projecteuler.net/

Title: Re: Interesting math questions
Post by: ruler501 on March 23, 2014, 12:14:16 am

willrandship I've looked at those but they are mostly number theory or discrete math problems and I'm more interested in topology and analysis.