Talk:Intersection of Empty Set

I'm having some trouble with this one. First, I think all the $$\bigcup$$s should be $$\bigcap$$s and that we should have $$\bigcap \mathbb S = \left\{{x: \forall X \in \mathbb S: x \in X}\right\}$$.

It also seems like this asserts that $$x \in \varnothing$$, which isn't true, is it? --Alec (talk) 02:17, 17 August 2010 (UTC)


 * D'oh. Corrected symbols on proof. Must have been half asleep.


 * Okay: so $$\left\{{x: \forall X \in \mathbb S: x \in X}\right\}$$ means:
 * "All the elements in the universe which are also in (all of the sets in $$\mathbb S$$)", or:
 * But all the elements in the universe are not in (all of the sets in $$\mathbb S$$).


 * It's an example of a vacuous truth. --prime mover 05:24, 17 August 2010 (UTC)


 * I think my real question is whether $$\mathbb S = \{\varnothing\}$$ or $$\mathbb S = \varnothing$$. That is, is it the empty set or the set containing the empty set?  --Alec  (talk) 01:32, 18 August 2010 (UTC)
 * $$\text{D}'\text{oh}^2$$.--prime mover 05:28, 18 August 2010 (UTC)