example of law of trichotomy on ¡

From the axiomatic definition of the real numbers, “ $<$ ” is a relation on $\mathbb{R}$ which satisfies the law of trichotomy. That is, for all $a,b\in\mathbb{R}$ , exactly one of the following is true:

•

$a<b$
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$b<a$
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$a=b$

As an axiom, this is sometimes expressed with $b=0$ . That is, for all $a\in\mathbb{R}$ , $a$ is either positive, negative, or zero.

Title	example of law of trichotomy on ¡
Canonical name	ExampleOfLawOfTrichotomyOn
Date of creation	2013-03-22 17:15:07
Last modified on	2013-03-22 17:15:07
Owner	me_and (17092)
Last modified by	me_and (17092)
Numerical id	5
Author	me_and (17092)
Entry type	Example
Classification	msc 06A05
Classification	msc 03E20