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On axiom of choice page I have encountered this formula:

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What does U-like symbol there means? It resembles union symbol, but union symbol should be used with two sets on the left and on the right. Then what does this symbol mean?

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4 Answers 4

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It is a union symbol. It is the union of all sets $S_i$, as $i$ ranges over all elements of the index set $I$.

$$\bigcup_{i\in I} S_i =\Bigl\{x\,\Bigm|\, \text{there exists }i\in I\text{ such that }x\in S_i\Bigr\}.$$

The symbol you describe is a special case, $$A_1\cup A_2 = \bigcup_{i\in\{1,2\}} A_i.$$

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It is the union symbol. In this context, it is the union of all sets $S_i$, with $i\in I$.

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This symbol is write the summation symbol, and represents a shorthand for union of many sets. In particular, $$\bigcup_{i=0}^nA_i = A_1\cup A_2\cup \cdots A_n$$

In your case, that means the union of all sets $S_i$ where $i$ is the element of $\mathcal I$.

Hope this helps. Ask anything if not clear :)

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It's the union of several sets. For example, if $\mathcal{I} = \{1,2,3\}$ then it would indicate $S_1 \cup S_2 \cup S_3$.

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