# Meaning of a union symbol in front of a set?

by df606
Tags: meaning, symbol, union
 P: 14 I'm trying to read this book "Automata, Computability, and Complexity" by Elaine Rich and on page 75 it defines this function: $\delta'(Q,c) = \cup\{eps(p):\exists q\in Q((q,c,p)\in\Delta)\}$ I've never seen the union operator used in this way. What does it mean? Apologies if this is in the wrong section. Edit: I don't care what the stuff inside the brackets means. I understand that part. I'm asking, what does $\cup$ mean when it's front of any set? It could be something like $\cup\{x:x\in\mathbb{R}\}$
 PF Patron Sci Advisor Thanks Emeritus P: 15,673 A union in front of a set is written when the elements in the set are sets themselves. So for example, we can have $$\bigcup \{A~\vert~A\in \mathcal{A}\}$$ this just means to take the union of each element in the set. That is: $$\bigcup_{A\in \mathcal{A}}{A}$$ Writing $\cup \{x~\vert~x\in \mathbb{R}\}$ doesn't make much sense since the element of $\mathbb{R}$ aren't sets (unless you see them as Dedekind cuts).
 P: 14 That explains things. Thanks!

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