Proposition: Transitivity of the Order Relation of Natural Numbers
For any natural numbers \(x,y,z\in\mathbb N\), the order relation obeys the following transitivity laws:
 If \(x < y\) and \(y < z\), then \(x < z\).
 If \(x \le y\) and \(y \le z\), then \(x \le z\).
 If \(x > y\) and \(y > z\), then \(x > z\).
 If \(x \ge y\) and \(y \ge z\), then \(x \ge z\).
Table of Contents
Proofs: 1
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Proofs: 1 2
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References
Bibliography
 Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008