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 …

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 ∞ ∞ or infinite cardinals …

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 …

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 …

May 3, 2020 · As far as I can tell, the "infinite matrix" representation of a linear operator is not that popular, especially in non-Hilbert contexts. There are many technicalities to address, as Jesko …

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...

4 You need to endow your infinite set with a measure such that the whole space has measure $1$ and then integrate (and hope that your function is measurable to begin with). For finite sets, …

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

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 …

Aug 20, 2015 · 24 I'm trying to show that one infinite always has a countably infinite subset, but I'm confused with something on the proof. Let S S be one infinite set. In that case, to show it …