What is infinity divided by infinity? - Mathematics Stack Exchange
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-big infinity, for
Existence of an infinite product that converges to a rational number ...
Mar 31, 2026 · 6 Informally, I would like to find an infinite product of rational numbers that evaluates to a nonzero rational number such that the multiplicity of each prime in the numerator is finite, while on …
Proof of infinite monkey theorem. - Mathematics Stack Exchange
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 …
What exactly is infinity? - Mathematics Stack Exchange
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 …
What is the difference between "infinite" and "transfinite"?
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 …
sequences and series - What is the sum of an infinite resistor ladder ...
Dec 10, 2023 · Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ .$ Taking the limit as $\ …
definition - Is infinity a number? - Mathematics Stack Exchange
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 …
Infinite Geometric Series Formula Derivation - Mathematics Stack …
The limit of the partial sums is the more rigorous way. You have to worry about convergence of the infinite sums to begin with otherwise. And doing it that way, you get an intermediate formula for the …
Understanding Euclid's proof that the number of primes is infinite.
Apr 7, 2016 · To his credit,he did not even say that. He said there was no largest prime because for any finite set of primes, there is a prime not in that set, It is logically quite different than asserting that …
Finding a basis of an infinite-dimensional vector space?
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, …