Set Complement/Examples

Examples of Set Complement

$\R_{>0}$ in $\R$

Let the universe $\Bbb U$ be defined to be the set of real numbers $\R$.

Let the set of (strictly) positive real numbers be denoted by $\R_{>0}$.

Then:

$\relcomp {} {\R_{>0} } = \R_{\le 0}$

the set of non-negative real numbers.

$\R_{>0}$ in $\C$

Let the universe $\Bbb U$ be defined to be the set of real numbers $\C$.

Let the set of (strictly) positive real numbers be denoted by $\R_{>0}$.

Then:

$\relcomp {} {\R_{>0} } = \set {x + i y: y \ne 0 \text { or } x \le 0}$