## When nothing is everything in Set theory

In an earlier post, I discussed the basic and most important aspects of Set theory, Functions and Real Number System. In the same, there was a significant discussion about the union and intersection of sets. Restating the facts again, given a collection $ \mathcal{A}$ of sets, the union of the elements of $ \mathcal{A}$ is defined by $ \displaystyle{\bigcup_{A \in \mathcal{A}}} A := {x : x \in A \textrm{ for at least one } A \in \mathcal{A} }$ . The…