# Trichotomy Property

## Enter two numbers below:

<-- Enter a number
<-- Enter a number.

Given a = 5, b = 6,:
Show the Trichotomy Property

## Definition

∀ ℝ a and b:
One of these is true:
1) a < b
2) a = b
3) a > b

## Prove one of the following:

5 < 6, 5 = 6, or 5 > 6

a - b = 5 - 6
a - b = -1

## Rearrange the equation:

a - b + b < b + 0
Therefore, a < b

## Simplifying, we get:

5 < 6 + 0
Therefore, 5 < 6
Therefore, a < b

5 < 6

5 < 6

### How does the Trichotomy Property Calculator work?

Demonstrates the Trichotomy Property with 2 numbers. Numerical Properties
This calculator has 2 inputs.

### What 2 formulas are used for the Trichotomy Property Calculator?

1. a < b, a = b, or a > b

For more math formulas, check out our Formula Dossier

### What 5 concepts are covered in the Trichotomy Property Calculator?

less than
Shows an inequality of one value being less than another
<
number
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
property
an attribute, quality, or characteristic of something
subtract
to take away from a group or a number of things
-
trichotomy property
for natural numbers a and b, either a is less than b, a equals b, or a is greater than b