> [!NOTE] Content on this page is adapted from [lecture notes](https://spakula.github.io/fyA/index.html) provided by [Ján Špakula](https://spakula.github.io) ## Inequalities For two numbers, $a$ and $b$: - $a<b$ means that $a$ is less than $b$ - $a > b$ means that $a$ is greater than $b$ - $a\leq b$ means that $a$ is less than or equal to $b$ - $a\geq b$ means that $a$ is greater than or equal to $b$ Note that $a>0$ means the same as "$a$ is positive". ### Axioms of inequalities 1. If $a<b$ then $a+c<b+c$ 2. If $a<b$ then $a-c<b-c$ 3. If $a<b$ and $c>0$ then $ac<bc$ 4. If $a<b$ and $c<0$ then $ac>bc$ ## Indices