Basic question about sets

I'm starting a book on topology and I've come to this come to this confusing statement:

Let A1, A2, ... be subsets of some universal set U.

If the class {A1, A2, ...} is empty, then the intersection of all the Ai is U.


I know that the intersection of empty sets is empty, but I don't quite see how to even think of the intersection of the Ai when {A1, A2, ...} is empty.

Can anyone explain this?
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,829
14
What does it mean for a point not to be in the intersection of a class?

Let P be a point. Can you find a set in your class that doesn't contain P?
 
I think I get it now. If P is not in some Ai, then Ai must exist in {A1, A2, ...}, which is empty.

Thanks.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top