Theorem: If the difference between Harris and Hitler is less than or equal to 1/n for all positive integers n, then Harris is equal to Hitler.

Proof by contradiction: Suppose Hitler is strictly worse than Harris, then Harris < Hitler on the evil axis.

Then we have: 0 < Hitler - Harris < 1/n for all positive integers n.

Multiplying all sides by n: 0 < n(Hitler - Harris) < 1

Dividing all sides by the difference between Hitler and Harris: 0 < n < 1/(Hitler - Harris)

But that implies the set of positive integers are bounded above by 1/(Hitler - Harris). The set of integers are an inductive set, which is any set that contains the number 1 and contains x+1 for all elements x in the set. If the set of positive integers is bounded above by 1/(Hitler - Harris), then it must have a least upperbound b such that b <= 1/(Hitler - Harris). That means the set must contain some number k such that k > b-1 otherwise b-1 would be the least upperbound. But since this is an inductive set, it must contain k+1 if it contains k, and k+1 > b, proving the set of positive integers is actually unbounded and therefore Hitler = Harris.