True or false? The following is a valid prof of the theorem that for every integer n, there is an integer k such that n < k < n + 2.

Assume n is an integer. Let k be an integer such that n < k < n + 2. This shows that for every n, an integer k such that n < k < n + 2. This shows that for every n, an integer k such that n < k < n + 2 exists.

True

False