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Bookmark or Share- Infinite monkey theorem and numbers - Mathematics Stack ExchangeI 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). I believe this experience can be reduced to choosing a random sequence among real numbers:, strictly speaking the monkey could type a sequence ...
- probability - Given an infinite number of monkeys and an infinite ...This is called the infinite monkey theorem in the literature. It follows from the second Borel-Cantelli lemma and is related to Kolmogorov's zero-one law , which is the result that provides the intuition behind general statements like this.
- Infinite monkey theorem: Average times a given string appears inThe monkey types one randomly selected character at a time. The set of characters is bounded, say e.g. the lowercase alphabet, or a set of M characters. I'm thinking that it's probably, for some example string e.g. "math", found by looking at the probability of "m" then "m being followed by a", then "ma being followed by t" and so on.
- Proof of infinite monkey theorem. - Mathematics Stack Exchange$\begingroup$ @AdityaAgarwal it is a theorem about a probability hence probabilty theory is the tool to use. Also, Borel-Cantelli is more or less equivalent to the infinite monkey theorem. The idea is to compare convergence of $1-\prod(1-p)$ with that of $\sum p$ $\endgroup$ –
- Are there similar theorems to the Infinite Monkey Typewriter Theorem?I was thinking about the Infinite Monkey Theorem and wondered if there’s any similar theorems but with a finite set? I know the infinite size is a critical assumption in the Monkey theorem, but are there any other results? UPDATE: I realize now this question was badly worded and unclear, so I'll state it a bit more thoroughly:
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