Pair Unions

Why

We often unite the elements of one set with another.

Discussion

Let $A$ and $B$ denote sets. We call $\cup \set{A, B}$ the pair union of $A$ and $B$. We denote the union of the pair $\set{A, B}$ by $A \cup B$. Clearly the pair union does not depend on the order of $A$ and $B$. In other words, $A \cup B = B \cup A$.

Facts

Here are some basic facts about unions of a pair of sets.¹ Let $A$ and $B$ denote sets.

1. Proofs will appear in the next edition. ↩︎