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 …

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 …

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 …

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 …

Nov 15, 2023 · (Context: the Infinite Monkey Theorem stipulates that given infinite time, a monkey can type out the complete works of Shakespeare, or any other text of finite length, just by …

Feb 9, 2020 · (A A is the infinite matrix with diagonal elements equal to 1 1 and 0 0 's everywhere else). If A A were finite-dimensional then mutlipyling the diagonal elements, the determinant …

Mar 28, 2023 · Imagine a sphere outline in an infinite void. If the area within the sphere outline is empty space, and the space outside is solid, it is a 3D shape of infinite volume, and since it …

as an example of an infinite degree algebraic field extension. I have done a cursory google search and thought about it for a little while, but I cannot come up with a less contrived example.

Jul 10, 2013 · Does the concept of an infinite composition of functions makes sense? In both cases of an countable infinite composition of functions and an uncountable infinite …