Definition:Ordering on Natural Numbers/Minimal Infinite Successor Set

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Definition

Let $\omega$ be the minimal infinite successor set.


The strict ordering of $\omega$ is the relation $<$ defined by:

$\forall m, n \in \omega: m < n \iff m \in n$


The (weak) ordering of $\omega$ is the relation $\le$ defined by:

$\forall m, n \in \omega: m \le n \iff m < n \lor m = n$