# 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

• $a=b$

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 ¡ ExampleOfLawOfTrichotomyOn 2013-03-22 17:15:07 2013-03-22 17:15:07 me_and (17092) me_and (17092) 5 me_and (17092) Example msc 06A05 msc 03E20