My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is

Feb 4, 2023 · In some of these infinite-dimensional vector spaces, when they're normed, there may be Schauder Bases , where we have infinite sums, which require a notion of convergence.

Aug 7, 2014 · 'every infinite and bounded part of $\mathbb {R^n}$ admit at least one accumulation point' because for me a set is either bounded so finite or infinite so unbounded. I don't really understand …

Apr 28, 2015 · 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 …

An infinite number? Kind of, because I can keep going around infinitely. However, I never actually give away that sweet. This is why people say that 1 / 0 "tends to" infinity - we can't really use infinity as a …

16 Once you have the necessary facts about infinite sets, the argument is very much like that used in the finite-dimensional case.

Nov 17, 2024 · How to solve dice problem using infinite series and combinations? Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago

Oct 9, 2025 · On the cardinality of Cartesian product of infinite sets Ask Question Asked 4 months ago Modified 4 months ago

Dec 15, 2025 · Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?

Jan 26, 2021 · I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $\\mathbb{R}^n$ when thinking about vector spaces.