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

1. Sep 9, 2011

### df606

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 $\cup\{x:x\in\mathbb{R}\}$

Last edited: Sep 10, 2011
2. Sep 10, 2011

### micromass

Staff Emeritus
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).

3. Sep 10, 2011

### df606

That explains things. Thanks!