The cardinality of the union of two infinite sets of equal cardinality 
Prove that if A is an infinite set and $|A| = |B|$ then $|A| = |A \cup B|$.

I don't know how to get an injection from $A∪B$ to $A$. I thought about considering $A\times B$, but don't see how that could work. 

$$|A |\leq|A \cup B|\leq|A| +| B|\leq 2|A |$$
Note that sin $A$ is infinite set so $2|A |=|A |$
