How do you simplify $\cup\{A, \cup A\}$? I want to simplify $\cup\{A, \cup A\},$ and also $\cup\cup\{A, \cup A\},$ so forth. I thought $\cup\{A, \cup A\}$ would not be simplified more. To say this in plain english, this union is a set that contains 1) all elements in $A$ and 2) all elements in all elements in $A,$ which I am not sure how to simplify. Then $\cup\cup\{A, \cup A\}$ is a set that contains all elements in the first union that I just described. Is it possible to simplify this union more? Thanks for your help.

You might or might not consider it a simplification, but, of course, $\bigcup \left\{A, \bigcup A\right\} = A \cup \bigcup A.$
