◀ ▲ ▶Branches / Number-systems-arithmetics / Proposition: Order Relation for Real Numbers is Strict and Total

Proposition: Order Relation for Real Numbers is Strict and Total

This order relation for real numbers defines a strict total order on the set of real numbers \(\mathbb R\), i.e.:

1. For any two elements \(x,y\in\mathbb R\) we have either \(x < y\) or \(y < x\) or \(x = y\) (but never more than one of these possibilities at the same time) trichotomy)
2. If \(x < y\) and \(y < z\) then \(x < z\) transitivity)
3. If \(x < y\) and \(y < z\) then \(x < z\) transitivity)

Table of Contents

Proofs: 1

Mentioned in:

Explanations: 1
Parts: 2
Sections: 3

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