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, …

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 regularized …

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...

Sep 24, 2020 · In the text i am referring for Linear Algebra , following definition for Infinite dimensional vector space is given . The Vector Space V(F) is said to be infinite dimensional vector space or infin...

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 closed in R.

Meaning of Infinite Union/Intersection of sets Ask Question Asked 8 years, 7 months ago Modified 4 years, 1 month 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.

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 somehow, which may …

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 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 Mathematicians …