Definition:Natural Numbers/Non-Zero

Definition
The natural numbers are often defined so as to exclude zero:

The set $\N \setminus \set 0$ is denoted $\N_{>0}$:
 * $\N_{>0} = \set {1, 2, 3, \ldots}$

1-Based Natural Numbers
The following axioms capture the behaviour of $\N_{>0}$, the element $1 \in \N_{>0}$, and the operations $+$ and $\times$ as they pertain to $\N_{>0}$:

Also see

 * Definition:Natural Number Addition