Give an example of a predicate P(n) about positive integers n, such that P(n) is

Question

Give an example of a predicate P(n) about positive integers n, such that P(n) is true for every positive integer from 1 to one billion, but which is never-the-less not true for all positive integers. (Hints: (1) There is a really simple choice possible for the predicate P(n), (2) Make sure you write down a predicate with variable n!) The purpose of this problem is to convince you that when checking a for all type proposition, it is not good enough to just check the truth for a few sample cases, or, for that matter, even a few billion sample cases. A general proof that covers all possible cases is necessary

Explanation / Answer

www.cs.utexas.edu/../predLogic.pdf

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