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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
infinity - What is the definition of an infinite sequence . . . Except for $0$ every element in this sequence has both a next and previous element However, we have an infinite amount of elements between $0$ and $\omega$, which makes it different from a classical infinite sequence So what exactly makes an infinite sequence an infinite sequence? Are the examples I gave even infinite sequences?
Infinite monkey theorem and numbers - Mathematics Stack Exchange I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books (here let's say the bible
elementary set theory - What is the definition for an infinite set . . . 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 definition is what is called a "weakly Dedekind-infinite set", and it sits somewhere between Dedekind-infinite and finite; that is, if a set is Dedekind
Given an infinite number of monkeys and an infinite amount of time . . . I doubt an infinite number of monkeys could even put together a full page full of nonsense but reasonable-length words with punctuation You could ask the same question about spiders Put an infinite number of spiders on typewriters and they won't produce Hamlet either, mostly because most spiders lack the strength to type
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, some of which, again, have easily describable bases
Does infinite equal infinite? - Mathematics Stack Exchange All three integrals are divergent and infinite and have the regularized value zero, but two of them are equal but not equal to the third one In other cases of divergent integrals or series, the regularized value and or growth rate (germ at infinity) or behavior at a singularity can differ as well or the differences can compensate for each
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