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"Any set called an index set is assumed to be non-void. Suppose T is an index set and for each t within T, A

_{t}is a set.

[inter] A

_{t}= {x : if t E T, x E A

_{t}}

t E T

= for each t within T, x is an element of A

_{t}"

There is also another expression with Union rather than Intersection, which I find more difficult to understand (U A

_{t}with tET written below U).

U = there exists t E T with x E A

_{t}

What is an index set?

Can someone explain this notation?

What is "t" - a number? a set? What does "there exists t E T with x E A

_{t}" mean?