Aug 11, 2012 · I know that $\\infty/\\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for

Nov 5, 2015 · 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

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 …

Mar 28, 2023 · Is there any pathological shape that has a finite surface area but an infinite volume, sort of like the opposite of a Gabriel's horn?

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 …

Dec 1, 2010 · Can you partition an infinite set, into an infinite number of infinite sets?

A decimal representation of a number has digits indexed by natural numbers. Which exactly is the position of that last 1 1? Is it the first after the decimal point? The second? The third? Each digit must …

Dec 16, 2012 · Can you ask given an infinite set about its cardinality? Does an infinite set have a cardinality? So, for example, what would be the cardinality of $+\\infty$?

Dec 1, 2014 · But the circumference also defines the subset with infinite area that lays "outside" (which is a conventional concept). That other "outside shape" would be an example of a finite-perimeter …

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.