Real Number

All numbers that lie on the numberline. Real Numbers are Complete

Definition

Let $a,b\in R$ Then $ab=0$ if and only if $a=0$ or $b=0$ Then $ab\ne 0$ if and only if $a\ne 0$ and $b\ne 0$

Alternate Definition

$\forall x,x^2\ge 0$

Properties of Real Numbers

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$ $\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$ $(\frac{a}{b})(\frac{c}{d})=\frac{ac}{bd}$ $\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}$