Apr 24, 2015 · The infinite monkey theorem states that if you have an infinite number of monkeys each hitting keys at random on typewriter keyboards then, with probability 1, one of them will type the …

Jun 6, 2020 · Infinite simply means "not finite", both in the colloquial sense and in the technical sense (where we first define the term "finite"). There is no technical definition that I am aware of for …

It is just what you want it to be, as long as it makes sense mathematically. We can talk about $+\infty$ and $-\infty$ in the extended real line, and about $\infty$ in the extended comlex plane. We can talk …

Dec 3, 2020 · However, while Dedekind-infinite implies your notion even without the Axiom of Choice, your definition does not imply Dedekind-infinite if we do not have the Axiom of Choice at hand: your …

Nov 18, 2023 · As for what infinite summation means ... Zeno's first paradox maps to this very problem. Infinite summation shows how an infinite number of terms can sometimes add up to a finite number. …

4 Infinity is not a number, but some things that can reasonably be called numbers are infinite. This includes cardinal and ordinal numbers of set theory and infinite non-standard real numbers, and …

Jan 26, 2021 · I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $\\mathbb{R}^n$ when thinking about vector spaces.

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 make any negative …

For many infinite-dimensional vector spaces of interest we don't care about describing a basis anyway; they often come with a topology and we can therefore get a lot out of studying dense subspaces, …

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 infinity as a …