Natural Numbers are Comparable/Strong Result/Proof 2

Theorem

Let $\N$ be the natural numbers.

Let $m, n \in \N$.

Then either:

$(1): \quad m + 1 \le n$

or:

$(2): \quad n \le m$


Proof


This theorem requires a proof.
In particular: Proof using Minimally Inductive Class under Slowly Progressing Mapping is Nest by exploiting Successor Mapping is Slowly Progressing.
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Sources

  • 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 9$ Supplement -- optional
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