Trichotomy Law for Real Numbers
That is, $\forall a, b \in \R$, exactly one of the following holds:
|\((1)\)||$:$||$a$ is greater than $b$:||\(\displaystyle a > b \)|
|\((2)\)||$:$||$a$ is equal to $b$:||\(\displaystyle a = b \)|
|\((3)\)||$:$||$a$ is less than $b$:||\(\displaystyle a < b \)|
This follows directly Real Numbers form Totally Ordered Field.
$\le$ is a total ordering on $\R$.
The trichotomy follows directly from Trichotomy Law.
The Trichotomy Law can also be seen referred to as the trichotomy principle.