6 Show that if a $\sigma$-algebra is infinite, that it contains a countably infinite collection of disjoint subsets. An immediate consequence is that the $\sigma$-algebra is uncountable.

I am looking for a small treatment of basic theorems about infinite products ; surprisingly enough they are nowhere to be found after googling a little. The reason for this is that I am beginning t...

De Morgan's law on infinite unions and intersections Ask Question Asked 14 years, 7 months ago Modified 4 years, 11 months ago

Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem?

Richard Thompson's groups $T$ and $V$ are well-known examples of infinite simple groups. See this answer of mine for more details, or look up the article Introductory notes on Richard Thompson's …

4 Infinity is not a number, but some things that can reasonably be called numbers are infinite. This includes cardinal and ordinal numbers of set theory and infinite non-standard real numbers, and …

Just out of curiosity, I was wondering if anybody knows any methods (other than the integral test) of proving the infinite series where the nth term is given by $\frac {1} {n^2}$ converges.

Suppose there is a family (can be infinite) of measurable spaces. What are the usual ways to define a sigma algebra on their Cartesian product? There is one way in the context of defining product

And you shouldn't say "infinite primes" when you mean "infinitely many primes". "Infinite primes" would be primes each one of which is infinite. In colloquial speech the word "infinite" may be used that way, …

My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is