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 …

Nov 15, 2023 · (Context: the Infinite Monkey Theorem stipulates that given infinite time, a monkey can type out the complete works of Shakespeare, or any other text of finite length, just by …

Mar 15, 2021 · I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books …

Oct 31, 2017 · Hence a vector space is infinite dimensional iff it has a basis which is infinite. If your infinite dimensional space has an inner product and is complete with respect to the …

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 …

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...

Aug 4, 2016 · 0 Since singletons in R are closed in usual topology. We can think about infinite class of singletons {x} where x belongs to (0,1] then there union will be (0,1] which is not …

Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university. By the way, there is a group of very strict …

What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago

Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 6 months ago Modified 4 years, 8 months ago