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 …

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 …

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 …

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 …

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...

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 …

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 …

Meaning of Infinite Union/Intersection of sets Ask Question Asked 8 years, 7 months ago Modified 4 years ago

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 …

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