- #1

- 2,111

- 18

[tex]

A_1\cup A_2\cup\cdots\cup A_n

[/tex]

and

[tex]

A_1\cap A_2\cap\cdots \cap A_n.

[/tex]

If we have an arbitrary collection of sets, [tex](A_i)_{i\in I}[/tex], then we can still write unions and intersections as

[tex]

\bigcup_{i\in I} A_i

[/tex]

and

[tex]

\bigcap_{i\in I} A_i.

[/tex]

If we have a finite amount of logical statements, then logical "or" and "and" of them can be written as

[tex]

A_1 \lor A_2\lor\cdots \lor A_n

[/tex]

and

[tex]

A_1 \land A_2\land\cdots \land A_n.

[/tex]

I don't think I've ever seen anything being done with arbitrary collections of logical statements. Have you? Is it okey to write something like this:

[tex]

\bigvee_{i\in I} A_i

[/tex]

and

[tex]

\bigwedge_{i\in I} A_i?

[/tex]