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.

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 …

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 …

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

Obviously it depends on the definition of "exists". Some authors explicitly work over the extended real line with ±∞ ± ∞ adjoined, so that such infinite limits do explicitly "exist" as first-class values. But …

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

Nov 28, 2018 · I am in need of examples of infinite groups such that all their respective elements are of finite order.

The term "infinite limit" is actually an oxymoron, like "jumbo shrimp" or "unbiased opinion". True limits are finite. However, it is okay to write down "lim f (x) = infinity" or "lim g (x) = -infinity", if the given …

+1 that's a great answer. Especially for the last point: I agree that Zeno's paradox is basically an example of how there can be infinitely many intervals in a finite period of time. I didn't know that there …