= Negative real number
{title2=$x<0$}
= Negative number
{synonym}
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 $-\sqrt2$; 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.
Back to article page
