Question: Find the error in the following "proof" that all positive integers n are equal. Let p(n) be the statement that all numbers in an n-element set of positive integers are equal. Then p(1) is true. Now assume p(n - 1) is true, and let N be the set of the first n integers. Let N be the set of the first n - 1 integers, and let N be the set of the last n - 1 integers. Then by p(n - 1) all members of N are equal and all members of N are equal. Thus the first n - 1 elements of N are equal and the last n - 1 elements of N are equal, and so all elements of N are equal. Thus all positive integers are equal.