- Proof of infinite monkey theorem. - Mathematics Stack Exchange
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 complete works of William Shakespeare
- general topology - Why is the infinite sphere contractible . . .
Why is the infinite sphere contractible? I know a proof from Hatcher p 88, but I don't understand how this is possible I really understand the statement and the proof, but in my imagination this
- set theory - Hilberts Grand Hotel is always hosting the same infinite . . .
From an excellent answer here, I gather that 1 is taken to mean that the hotel is hosting an infinite set of guests and that 2 means things have changed, we now have to reassign every room again to accommodate a new infinite set of guests (eg: the ones before + 1) I saw other threads and answers But the "new" set is just the same old set
- elementary set theory - What do finite, infinite, countable, not . . .
What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
- 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 who find it very difficult to accept the manipulation of infinite quantities in any way
- calculus - Infinite Geometric Series Formula Derivation - Mathematics . . .
Infinite Geometric Series Formula Derivation Ask Question Asked 12 years, 7 months ago Modified 4 years, 9 months ago
- If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
6 Show that if a $\sigma$-algebra is infinite, that it contains a countably infinite collection of disjoint subsets An immediate consequence is that the $\sigma$-algebra is uncountable
- What is the difference between infinite and transfinite?
The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about $\infty$ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes
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