Research \"Infinite Monkey Theorem\". This is an NP-hard combinatorial and proba

Question

Research "Infinite Monkey Theorem". This is an NP-hard combinatorial and probability problem. This is a theorem, meaning that it has been proven. That is not the same as saying it has been demonstrated. In fact, for this theorem to be demonstrable, we would require “infinite” time and true “randomness” to give us “almost surely” results. You will notice that absent of our requirements is “intent.” Now, if our conditions are met, a consequence is inevitably that the works of Shakespeare’s “Hamlet”, John Milton’s “Paradise Lost”, and—yes—even the Holy Bible could be reproduced at random. So, why are these requirements so important?

Discuss the concepts: infinite, random, and almost surely. Understand that these terms each have rigid mathematical meaning. How are these concepts relevant to the study of combinatorics, and why can we rest assured that none of the above works of literature were produced at random?

Explanation / Answer

The concept of infinite in mathematics refers to something larger than what one can think. For infinite time experiments, infinite refers to a very large time such that if the eperiment is held for that time then we can expect the results of the experiment to be the same as expected.

Randomness refers to no specific preference or choice in choosing events. Hence occuring of all events are equally likely and we cannot preconcieve it.

Almost usrely refers to being almost sure about the event to occur or the probability of that event to occur under the given conditions is almost equal to 1. When the experiment is carried till infinity then it is likely that every possible random event associated shall almost surely occur

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