1. ## Defining Big Intersection

Hi guys.
I completely understand the definition for the intersection between two or more sets, but this definition just does not make sense.

If M is a set of sets. For all A which are an element of M, x is an element of A. Isn't that the exact same thing as the union? Am I reading this wrong? I don't see how this definition covers the fact that x HAS to appear in EVERY A. It just states that x is an element of A, not every A.

2. ## Re: Defining Big Intersection

I hope I dont say anything wrong, but this is my take on it:

You have a non empty set M. The intersection of M is the set of elements, which are in EVERY set of elements of M. Thats why there is a ∀. You just look specifially at the intersection only and not any other parts of sets. I guess thats what confuses you.

3. ## Re: Defining Big Intersection

Thanks. I was just reading the statement wrong, separating the two properties.

4. ## Re: Defining Big Intersection

$\bigcap M = \left\{ {x : (\forall A \in M)\left[ {x \in A} \right]} \right\}$ and $\bigcup {M = \left\{ x: (\exists A \in M)\left[ {x \in A} \right]} \right\}$
Note in the first it is $\forall A \in M$ but in the second it is $\exists A \in M$.