Basic Laws of Inequality

For any real numbers $a$, $b$ and $c$.

1. Transition law

   If $a>b$ and $b>c$, then we have $a>c$.

2. Addition law

   If $a>b$, then we have $a+c>b+c$.

3. Multiplication law
   1. If $a > b$ and $c > 0$, then we have $ac > bc$.
   2. If $a > b$ and $c < 0$, then we have $ac < bc$.
4. Inverse law
   1. If $a > b > 0$, then $\dfrac{1}{b}>\dfrac{1}{a}>0$.
   2. If $a < b < 0$, then $\dfrac{1}{b}<\dfrac{1}{a}<0$.
5. Non-negative law

   For any real number $a$, $a^2 \ge 0$.

Same Topic:

1. Definitions Identities of Squares Measurement of Sound Quadratic Inequality