Wdproof11

Proof by Will Dyer

Given: 0 < 1 < 2 < …

Proof: Let X be a subset of N that has no least value, and X^{C} be the complement of X in N. Now suppose all natural numbers less than or equal to k are in X^{C}. Therefore, if k+1 is in X, k+1 is the least value of X. This cannot be, since X has no least value, so k+1 is in X^{C}. By strong induction, X^{C} = N and X is the empty set.

page revision: 1, last edited: 28 Feb 2018 18:17