# Trichotomy Property

Look how easy this is:

Example 1: given two numbers 5 and 7

Can more than one statement be true? No. 5 can not be equal to or greater than 7.

Example 2: Todd has 4 apples and Jorge has 10 apples. Which statement is true?

- Todd has more apples than Jorge.
- Todd has the same amount of apples as Jorge.
- Todd has fewer apples than Jorge.

Example 3: Amanda scored more points in basketball than Lauren. What else could we say about the scores?

- Lauren could NOT have scored more than Amanda
- Lauren could NOT have scored the same amount as Amanda.

Let's sum this up by using variables (letters instead of numbers). Only one statement can be true about any 2 numbers

**a**and

**b**.

a < b a = b or a > b

One last example: Alex is shorter than Barry. It follows than Barry is taller than Alex and they cannot be the same height.

**Related Links:**

Math

algebra

Inverse Properties of Addition and Multiplication

Distributive Property

To link to this **Trichotomy Property** page, copy the following code to your site: