Corollary: Order Relation for Natural Numbers is Strict Total
(related to Proposition: Comparing Natural Numbers Using the Concept of Addition)
The order relation for natural numbers "$<$" defines a strict total order on the set $\mathbb N$ of natural numbers, i.e. for any natural numbers \(x,y,z\in\mathbb N\), we have
- Only one of the following cases can be true: either \(x=y\), or \(x > y\), or \(x < y\) trichotomy).
- If $x < y$ and $y < z$, then $x < z$ transitivity).
- The same applies for the relation "$ > $".
Table of Contents
Proofs: 1
Mentioned in:
Explanations: 1
Proofs: 2 3 4
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References
Bibliography
- Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008
