Definition:Ordering on Natural Numbers/1-Based

Definition

Let $\N_{>0}$ be the axiomatised $1$-based natural numbers.

The strict ordering of $\N_{>0}$, denoted $<$, is defined as follows:

$\forall a, b \in \N_{>0}: a < b \iff \exists c \in \N_{>0}: a + c = b$

The (weak) ordering of $\N_{>0}$, denoted $\le$, is defined as:

$\forall a, b \in \N_{>0}: a \le b \iff a = b \lor a < b$