Thread: Set theORY

denotes the set
for any non-empty set S

And
denotes the set
for any set S
Does anyone know how to explain waht it's mean?
Can it be explain using Venn Daigaram?

Originally Posted by Singular

denotes the set

Here we are considering a set S whose elements are sets. this symbol denotes the set of all elements that fall in the intersection of the sets contained in S. So any element that is in EVERY set in S will be in the set

for any non-empty set S

And
denotes the set

this again is talking about a set S whose elements are sets. any element that is in the union of all the sets will be in , that is any element that is in ANY set will be in the set

Can it be explain using Venn Daigaram?

I've never actually seen these represented using Venn Diagrams, but it may be possible. In the class I took we used a kind of number line approach