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The $()^c$ means the complement of whatever there's in the bracket in respect to $\Omega$

i just want to know what this big U and the flipped U means. Also what's the Latex-Symbol?


closed as off-topic by user99914, NCh, Deepesh Meena, Lord Shark the Unknown, max_zorn Sep 11 '18 at 4:23

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  • 2
    $\begingroup$ Union and intersection of a family of sets $\endgroup$ – A.Riesen Jul 2 '16 at 5:01
  • 4
    $\begingroup$ Did you do any research before posting? What does your book say when it defines the complement notation? What does your book say in its symbol index? Did you Google "set notation," or read the Wikipedia article on mathematical notation? $\endgroup$ – user296602 Jul 2 '16 at 5:05
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    $\begingroup$ -1 for laziness. This is a question much better answered by Google, Wikipedia, Detexify, etc. $\endgroup$ – anomaly Jul 2 '16 at 5:15
  • $\begingroup$ @anomaly thanks for the hint of Detexify, i did'nt knew about that. $\endgroup$ – SAJW Jul 2 '16 at 5:16
  • $\begingroup$ LaTeX: \bigcap and \bigcup. $\endgroup$ – lemontree Jul 2 '16 at 16:06

If $\mathcal{M}$ is a collection of sets, then $\bigcup_{M\in\mathcal{M}} M$ denotes the union of all the elements of $\mathcal{M}$. For instance, if $\mathcal{M}=\{A,B,C\}$, then $\bigcup_{M\in\mathcal{M}} M=A\cup B\cup C$. More precisely, $$\bigcup_{M\in\mathcal{M}} M=\{x:\text{there exists } M\in\mathcal{M}\text{ such that }x\in M\}.$$

Similarly, $\bigcap_{M\in\mathcal{M}} M$ denotes the intersection of all the elements of $\mathcal{M}$. The LaTeX command for $\bigcup$ is \bigcup and the command for $\bigcap$ is \bigcap.

More generally, $$\bigcup_{M\in\mathcal{M}}[\text{some expression involving $M$}]$$ denotes the union of the expressions for all elements $M$ of $\mathcal{M}$. So in your example, $\bigcup_{M\in\mathcal{M}} M^c$ denotes the union of all the complements of elements of $\mathcal{M}$. You should think of this similar to summation notation, except you are taking a union instead of a sum.


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