0

I'm going through a book on math proofs and I'm struggling to understand these definitions:

https://ibb.co/Lzrnt3J

When I'm going through the definition of ⋂ F, what's going through my head is "For all sets A, if A is in the family of sets F, then x is an element of A." I feel like my understanding is shaky on that one, but it makes sense.

Where I'm really struggling is the definition of ⋃ F. I'm thinking "There exists a set A in a family of sets F and x is an element of A." Am I correct in thinking about it that way? If so, how is that a definition of ⋃ F?

My goal in this post is to receive as much correction in my understanding of these definitions as possible. Any help is appreciated. Thanks.

José Carlos Santos
  • 427,504
Faith Alone
  • 551

1 Answers1

1

$x\in\bigcup F$ means there is some $A\in F$ for which $x\in A.$
"Some" means at least one, but possibly more than one.

$x\in\bigcap F$ means for every $A\in F,$ $x\in A.$

That is how this notation is used in set theory, but most mathematicians write $\displaystyle \bigcup_{A\,\in\,F} A$ or a similar thing rather than $\bigcup F.$ (And similarly for intersections.)

Michael Hardy
  • 1