More odds and evens

an odd number of ones.

Let En be the set of`binary strings of length n with

an even number of ones.

We have already presented an algebraic

proof that On =En

An elegant combinatorial proof can be had by

putting On and En in one-to-one correspondence.

The correspondence principle says that

if two sets can be placed in one-to-one

correspondence, then they are the same size!