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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
- 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
- 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?
- 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
- set theory - Hilberts Grand Hotel is always hosting the same infinite . . .
A bit background: This article says that "The mathematical paradox about infinite sets" envisages Hilbert's Grand Hotel: " a hotel with a countable infinity of rooms, that is, rooms that can be placed in a one-to-one correspondence with the natural numbers
- Types of infinity - Mathematics Stack Exchange
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 can easily see that there are infinite types of infinity via Cantor's theorem which shows that given a set A, its power set P (A) is strictly larger in terms of infinite size (the
- 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
- Condition for infinite solutions to matrix linear equation.
For a matrix equation AX=B it is known that a there are infinite solutions for the matrix X if |A|=0 (adj A)B = O Consider the following situation Satisfies the condition for infinite solutions,
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