Set Complement/Examples
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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:
- $\relcomp {} {\R_{>0} } = \set {x + i y: y \ne 0 \text { or } x \le 0}$