For the statement to be true, we need it to be the case that no matter what natural number we select, there is always some natural number that is strictly smaller. Perhaps we could let \(y\) be \(x-1\text{?}\) But here is the problem: what if \(x = 0\text{?}\) Then \(y = -1\) and that is not a number! (in our domain of discourse). Thus we see that the statement is false because there is a number which is less than or equal to all other numbers. In symbols,