Trichotomy Property

The Trichotomy Property means that when you are comparing 2 numbers, one of the following must be true: the first number is bigger than the second number, the first number is smaller than the second number or the two numbers are equal. This is a common sense property with a hard name
Look how easy this is:

Example 1: given two numbers 5 and 7

  • 5 is less than 7     5 < 7

  • 5 is equal to 7       5 = 7

  • 5 is greater than 7     5 > 7

  • Which statement is true? 5 is less than 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:
    Inverse Properties of Addition and Multiplication
    Distributive Property

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