$\left\{a\right\}\cup\left\{b\right\}\cup\left\{c\right\}$ can be written as $\bigcup\left\{\left\{a\right\},\left\{b\right\},\left\{c\right\}\right\}$ can it not?
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2Yes, it can be written that way. – Ethan Bolker May 22 '17 at 12:52
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Indeed. Generally, $\bigcup \mathscr A = \bigcup\limits_{A\in\mathscr A}A$ where $\mathscr A$ is a family of sets. – MPW May 22 '17 at 13:03
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it is the other way around :) that is, $\bigcup{{a},{b},{c}}$ could be written as ${a}\cup{b}\cup{c}$ – Mirko May 22 '17 at 17:04
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Yes. More generally, for any sets $A,B,C,$ $$ \bigcup\{A,B,C\}=A\cup B\cup C.$$ And of course the same goes for any number of sets.
bof
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