May 12, 2024 · Except for $0$ every element in this sequence has both a next and previous element. However, we have an infinite amount of elements between $0$ and $\omega$, which makes it …

For many infinite-dimensional vector spaces of interest we don't care about describing a basis anyway; they often come with a topology and we can therefore get a lot out of studying dense subspaces, …

Apr 24, 2015 · The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the …

Aug 13, 2023 · From an excellent answer here, I gather that 1. is taken to mean that the hotel is hosting an infinite set of guests and that 2. means things have changed, we now have to reassign every …

Why is the infinite sphere contractible? I know a proof from Hatcher p. 88, but I don't understand how this is possible. I really understand the statement and the proof, but in my imagination this...

What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 3 months ago Modified 13 years, 3 months ago

Oct 4, 2020 · I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition. You can never make any negative …

Multiplication of infinite series Ask Question Asked 11 years, 9 months ago Modified 4 years, 9 months ago

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.

Dec 3, 2020 · However, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand: your …