Nov 6, 2013 · In fact, more is known: Theorem: Every (Hausdorff) countable compact is homeomorphic to a subspace of Q Q. Essentially, it is a consequence of Sierpinski …

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 …

Many texts reads "It is well known that for infinite matrices multiplication is non-associative". A treatise on this can be found in On the associativity of infinite matrix multiplication. However...

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?

Jan 2, 2015 · I am wondering if we just showed that any infinite set of sets contains an infinite restriction. So that the sigma algebra component isn't needed for the next iteration.

Oct 2, 2015 · Similarly, to disprove infinite intersection of open sets is open, it is enough to give a particular collection of open sets such that intersection is not open.

Dec 5, 2015 · I am having trouble with the following terms: countably infinite, uncountable, and finite. In addition, for the following problems I need to select which category they fall into. $1)$ …

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 …

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

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 …