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 …

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 …

A treatise on this can be found in On the associativity of infinite matrix multiplication. However, if x x and v v are infinite vectors, and A A is a semi-infinite matrix, then Does the product x⊺Au x ⊺ …

Sep 11, 2011 · the set of all infinitely long sequences of real numbers The first is a finite-dimensional vector space. The next three are infinite-dimensional vector spaces. They're not …

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.

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.

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 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. $1)$ …

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

Sep 16, 2017 · Here "infinite grade" refers to infiniteness of the complement. He proves (§110, p108) that the only subgroup of the group of permutations of I I that is infinitely transitive of …