/sci/ - Science & Math

I'm confused. If you say [math]p\neq 1[/math], then wouldn't you have to say [math]n\neq 1[/math] in this case too? As in every natural number BUT 1 can be represented as a product of prime numbers (as [math]1\in\mathbb{N}[/math] too but [math]p\neq 1[/math], hence it can't be represented as a product [math]p_1 \cdots p_k[/math]).