# Union-like symbol meaning

On axiom of choice page I have encountered this formula:

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?

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, $$A_1\cup A_2 = \bigcup_{i\in\{1,2\}} A_i.$$

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

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 :)

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