Lemma 2.3.3 (Positive natural numbers have no zero divisors). Let \(n, m\) be natural numbers. Then \(n \times m = 0\) if and only if at least one of \(n, m\) is equal to zero. In particular, if \(n\) and \(m\) are both positive, then \(nm\) is also positive.
\(Proof\). See Exercise 2.3.2.