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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

1. Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008