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
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 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 …
elementary set theory - What is the definition for an infinite set ...
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 …
calculus - Infinite Geometric Series Formula Derivation - Mathematics ...
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 …
How can Cyclic groups be infinite - Mathematics Stack Exchange
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 …
One divided by Infinity? - Mathematics Stack Exchange
Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university. By the way, there is a group of very strict Mathematicians …
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 …
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, …
Types of infinity - Mathematics Stack Exchange
Dec 18, 2012 · Not only infinite - it's "so big" that there is no infinite set so large as the collection of all types of infinity (in Set Theoretic terms, the collection of all types of infinity is a class, not a set). You …