02-26-2011, 11:54 AM
Here is a nice accessible introduction to infinity:
http://www.mathacademy.com/pr/minitext/infinity/
It says "The trouble here is in thinking that an infinite set must contain everything. However, a little thought shows that this needn't be true."
Of relevance to the discussion here is Cantor's theorem, which essentially says that for any infinite set one can always find a set that is bigger. Sort of like no matter how good you are at playing tennis, there is always someone better (unless you are Roger Federer). So, even if you proposed that the universe contained everything, I could always find something that it didn't contain! (this statement, while paradoxical, is nonetheless mathematically sound).
http://www.mathacademy.com/pr/minitext/infinity/
It says "The trouble here is in thinking that an infinite set must contain everything. However, a little thought shows that this needn't be true."
Of relevance to the discussion here is Cantor's theorem, which essentially says that for any infinite set one can always find a set that is bigger. Sort of like no matter how good you are at playing tennis, there is always someone better (unless you are Roger Federer). So, even if you proposed that the universe contained everything, I could always find something that it didn't contain! (this statement, while paradoxical, is nonetheless mathematically sound).