Definition:Ordering on Natural Numbers/Von Neumann Construction
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Definition
Let $\omega$ denote the set of natural numbers as defined by the von Neumann construction.
The strict ordering of $\omega$ is the relation $<$ defined by:
- $\forall m, n \in \omega: m < n \iff m \subsetneqq n$
The (weak) ordering of $\omega$ is the relation $\le$ defined by:
- $\forall m, n \in \omega: m \le n \iff m \subseteq n$
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 5$ Applications to natural numbers: Definition $5.1$