Let a and b be as you describe (hash collision), and suppose that collisions are extremely rare. We have a theorem that a=b => a+1=b+1. But in this case, a=b ac

Let a and b be as you describe (hash collision), and suppose that collisions are extremely rare. We have a theorem that a=b => a+1=b+1. But in this case, a=b according to our hash-equality, but a+1!=b+1, which contradicts the theorem we've already proved. for real problems with my statement, see your sibling comment.