I think I understand now. Since the intersection over \mathcal{A} is defined as \left\{x: (\forall A)(A\in \mathcal{A} \Rightarrow x\in A)\right\} and the antecedent of the conditional is always false (there is nothing in \mathcal{A}), the conditional will always be true, because of the way the...
I am beginning to study set theory and came across the following example:
Let \mathcal{A} be the empty family of subsets of \mathbb{R}. Since \mathcal{A} is empty, every member of \mathcal{A} contains all real numbers. That is, ((\forall A)(A\in\mathcal{A}\Rightarrow x\in A)) is true for...