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 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 …

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 …

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 …

Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 3 months ago Modified 4 years, 5 months ago

Can you give me an example of infinite field of characteristic p ≠ 0 p ≠ 0? Thanks.

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 …

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.

6 Show that if a σ σ -algebra is infinite, that it contains a countably infinite collection of disjoint subsets. An immediate consequence is that the σ σ -algebra is uncountable.

Then prove that it holds for an index set of size n + 1 n + 1 and wrap it up by n → ∞ n → ∞ but I'm not convinced that's right. For example, an argument like that doesn't work for countable …