Question

what is law of trichotomy

Answer 1

In mathematics trichotomy states that every real number is either positive , negative or zero

Answer 2

The law of Trichotomy states that in the set of all real numbers, every number is either negative, zero or positive.

It can also be mentioned in another way:  For every pair of two real numbers x, y  exactly one of the following is true: 
       x < y,   x = y   OR   x > y.

These can be specified in more mathematical notations. The essence is that.