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 …

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

All three integrals are divergent and infinite and have the regularized value zero, but two of them are equal but not equal to the third one. In other cases of divergent integrals or series, the …

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

Nov 17, 2021 · $\begingroup$"I assume that only uncountably infinite unbounded sets have infinite measure" - This is true in the Lebesgue measure on $\Bbb R$. Any countable set, …

A set X is countably infinite if there exists a bijection between X and $\mathbb {Z}$. To prove a set is countably infinite, you only need to show that this definition is satisfied, i.e. you need to …

Multiplication of infinite series Ask Question Asked 11 years, 8 months ago Modified 4 years, 8 months ago

Jun 6, 2020 · The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals …

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 20, 2015 · 28 Welcome to the wormhole. A set which has a countably infinite subset is called Dedekind Infinite. It is not provable within Zermelo-Fraenkel set theory (ZF) that every infinite …