In classical logic, this axiom of trichotomy holds for ordinary comparison between real numbers and therefore also for comparisons between integers and between rational numbers.

What is the property of trichotomy?

noun Mathematics. the property that for natural numbers a and b, either a is less than b, a equals b, or a is greater than b. Also called law of trichotomy, trichotomy law, trichotomy principle.

What is trichotomy property of inequality?

The Trichotomy Property and the Transitive Properties of Inequality. Trichotomy Property: For any two real numbers a and b, exactly one of the following is true: a < b, a = b, a > b. ... Note: These properties also apply to "less than or equal to" and "greater than or equal to": If a≤b and b≤c, then a≤c.