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

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 …

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 …

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 …

Feb 4, 2023 · While in infinite dimensional spaces it may be infinite in cardinality, the sums $$ \Sigma_ {i=1}^n b_iv_i $$ , will be finite sums; sums over finite subsets of our infinite basis.

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 …

Jan 12, 2011 · Just get an infinite number of monkeys (or a slightly smaller number of computers) and opening a publishing business. Make a million bucks and retire. But this rings false, especially since …

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 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 …

0 There is a way of proving that there is "infinite number of sides in a circle", in the following sense. Infinity was a number to both Kepler and Leibniz who spoke of a circle as an infinite-sided polygon. …