Negative real number ($x<0$)

A negative real number is a real number $x<0$, lying to the left of zero on the number line. Equivalently, $x=-a$ for a positive real number $a$. Examples include $-3$, $-1/2$ and $-\sqrt{2}$; zero is excluded.

The sum of two negative real numbers is negative, while their product is positive. Multiplication by a negative real number reverses an inequality: if $x<y$ and $c<0$, then $cx>cy$. These are consequences of compatibility between the total order and the arithmetic of an ordered field, rather than independent rules about written minus signs.