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Meaning of a union symbol in front of a set?

by df606
Tags: meaning, symbol, union
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df606
#1
Sep9-11, 05:59 PM
P: 14
I'm trying to read this book "Automata, Computability, and Complexity" by Elaine Rich and on page 75 it defines this function: [itex]\delta'(Q,c) = \cup\{eps(p):\exists q\in Q((q,c,p)\in\Delta)\}[/itex]
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 [itex]\cup[/itex] mean when it's front of any set? It could be something like [itex]\cup\{x:x\in\mathbb{R}\}[/itex]
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micromass
#2
Sep10-11, 08:31 AM
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A union in front of a set is written when the elements in the set are sets themselves. So for example, we can have

[tex]\bigcup \{A~\vert~A\in \mathcal{A}\}[/tex]

this just means to take the union of each element in the set. That is:

[tex]\bigcup_{A\in \mathcal{A}}{A}[/tex]

Writing [itex]\cup \{x~\vert~x\in \mathbb{R}\}[/itex] doesn't make much sense since the element of [itex]\mathbb{R}[/itex] aren't sets (unless you see them as Dedekind cuts).
df606
#3
Sep10-11, 01:01 PM
P: 14
That explains things. Thanks!


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