induction

ITT some proof by induction.

Claim: For every positive integer n, n is equal to every positive integer less than n.

Proof: For n = 1, there are no positive integers less than 1 so the claim holds trivially. Suppose the claim holds for some fixed n, i.e. that n = n - 1 = ... = 1. Adding 1 to the leftmost equality from this, n = n - 1, it follows that n + 1 = n, so n + 1 = n = n - 1 = ... = 1. Therefore the claim holds for n + 1. QED

There is only one positive integer.