The union of two sets $A$ and $B$, denoted $A\cup B$, is the set of things which are either in $A$ or in $B$ or both.

Formally stated, where $C=A\cup B$

$$x\in C\leftrightarrow (x\in A\vee x\in B)$$

That is, Iff $x$ is in the union $C$, then either $x$ is in $A$ or $B$ or possibly both.

Examples

• $\{1,2\}\cup \{2,3\}=\{1,2,3\}$
• $\{1,2\}\cup \{8,9\}=\{1,2,8,9\}$
• $\{0,2,4,6\}\cup \{3,4,5,6\}=\{0,2,3,4,5,6\}$
• $R^{-}\cup R^{+}\cup \left\{0\right\}=R$ (In other words, the union of the negative reals, the positive reals and zero make up all of the real numbers.)