# Mathematical notation

• Mathematica
Yegor
T is an index set. And for each $$t \in T$$ $$A_t$$ is a set
$$\bigcup_{t \in T} A_t = \{x : \exists t \in T with x \in A_t \}$$
What means this $$\bigcup$$ symbol and entire expression?
And question on index set: is it used just for orderring any other set?

Homework Helper
It's the union. If A and B are sets, $A\cup B$ denotes the union of A and B. It's that set which contains all the elements of A and those of B. So
$$A \cup B = \{x|x\in A \vee x\in B\}$$

To generalize this to a union of an arbitrary number of sets is easy. That's exactly what your expression is: the union of all $A_t$.

Yegor
thank you very much, Galileo!