Some Inequality Notations

Definition

Let $a,b\in \mathbb{R}$.

• If $a-b\in \mathbb{P}$, then we write $a>b$ or $b<a$
• If $a-b\in \mathbb{P}\cup \{0\}$, then we write $a\ge b$ or $b\le a$

Based on the Tricothomy Property, if both $a\le b$ and $a\ge b$, then $a=b$.

For notational convenience, we can write $a<b$ and $b<c$ as $a<b<c$. Also applies to the “or equal to” notation.