# Basic Set Theory/Topology

1. Dec 7, 2005

### JasonRox

The book that I'm reading is saying...

If C is the null collection of subsets of S then,

(Union) C = Null

(Disjoint) C = S

Is this true?

2. Dec 7, 2005

### Enuma_Elish

How does your book define a null collection of subsets?

3. Dec 7, 2005

### matt grime

Take it as a definition, or read this, for example:

since i presume by (disjoint) you actually mean intersection.

incidentally i got that answer by insertingf the words empty intersection into google and clicking the first link.

you might want to remember that the next time you struggle to check a definition,

Last edited: Dec 7, 2005
4. Dec 7, 2005

### JasonRox

The truth is that I searched and searched. Then I thought and thought, then searched again.

Using the definition it is true, and I see that, but I was skeptical about it.

Last edited: Dec 7, 2005
5. Dec 7, 2005

### mathwonk

imagine a list of rules for a game which has no rules at all!!

the intersection of a null collection of sets, corresponds to those moves which satisfy all the rules, hence any move at all, i.e. S.

etc....you do the other case

6. Dec 31, 2005

### inquire4more

7. Dec 31, 2005

### HallsofIvy

Staff Emeritus
if x is in (Union)C, then it must be in at least one of the members of C. But C has no members so that is always false. Yes, (Union) C= Null set.

By (Disjoint) C do you mean the intersection[\b] of all the members of C?

Let x be any member of S. If x is NOT in (intersection) C, then there must be some member of C such that x is NOT in it. But that's NEVER true because C has no members! Therefore every member of S is in (Intersection) C.