# Union

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 $$C = A \cup B$$

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

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

todo: more lengthy ex­pla­na­tion for Math 2 level

# Examples

• $$\{1,2\} \cup \{2,3\} = \{1,2,3\}$$

• $$\{1,2\} \cup \{8,9\} = \{1,2,8,9\}$$

• $$\{0,2,4,6\} \cup \{3,4,5,6\} = \{0,2,3,4,5,6\}$$

• $$\mathbb{R^-} \cup \mathbb{R^+} \cup \{0\} = \mathbb{R}$$ (In other words, the union of the nega­tive re­als, the pos­i­tive re­als and zero make up all of the real num­bers.)