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We have $C_x \subseteq X$ for every $x \in X$. So we have the following $$\bigcup_{x \in X} C_x \subseteq X.$$

I don't know what it means, mainly the left part in the displayed formula. The $C_x$ is an equivalence class, but what does $\bigcup_{x \in X} C_x$ mean?

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    It is the `union` of all the $C_x$, for $x\in X$. – 2017-01-23
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    $\cup_{x\in X}C_x$ is the union of all sets $C_x$, with $x\in X$ – 2017-01-23

1 Answers 1

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$$\color{silver}{\Big(~}\bigcup_{x\in X} C_x\color{silver}{~\Big)}~\subseteq X$$

Note: The cup is associated with the term $C_x$, not the statement as a whole.

$C_x$ presumably represents a set generated by some construction rule based on an element $x$.

$\bigcup_{x\in X} C_x$ is then the union of all such sets, $C_x$, each generated by the elements of $X$.

The statement asserts that this union is a subset of $X$ (or equal to $X$).