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 …

The other day, my teacher was talking infinite-dimensional vector spaces and complications that arise when trying to find a basis for those. He mentioned that it's been proven that some (or …

Dec 1, 2017 · Lemma An infinite cyclic group has infinitely many (cyclic) subgroups. Proof: An infinite cyclic group is isomorphic to additive group Z Z. Each prime p ∈ Z p ∈ Z generates a …

Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 2 months ago Modified 4 years, 5 months ago

A set A A is infinite, if it is not finite. The term countable is somewhat ambiguous. (1) I would say that countable and countably infinite are the same. That is, a set A A is countable (countably …

The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions. This was discussed on MO but I can't find the thread.

Aug 12, 2015 · However, it then simply states that these three spaces are infinite-dimensional normed vector spaces. The only thing mentioned in my notes so far is in relation to finite …

Jun 6, 2020 · The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about ∞ ∞ or infinite cardinals …

Oct 4, 2020 · I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition. You can never …

An infinite union of closed sets is a closed set? Ask Question Asked 12 years, 2 months ago Modified 6 months ago