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)