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 …

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

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

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

Mar 25, 2023 · 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) = …

Aug 12, 2015 · It is well known that in the case of a finite interval $[0,1]$ with a partition of equal size $1/n$, we have: $$\\lim_{n\\rightarrow \\infty} \\frac{1}{n}\\sum_{k=0 ...

May 10, 2021 · Write out a few terms of the series. You should see a pattern! But first consider the finite series: $$\sum\limits_ {n=1}^ {m}\left (\frac {1} {n}-\frac {1} {n+1 ...

+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 …