empty set?

by pivoxa15
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P: 2,268
 Quote by matt grime I doubt you have used it correctly becuase you appear to have several lines of proof. It is not a definition that the empty set is a subset of everything, it is a (vacuously) true deduction (in any reasonable logic). If it weren't a subset of X, say, then there is an e in E (empty set) that is not in X. But that is false - there is no e in E since E is empty. I don't see that there is anything to prove at all. The complement of U is the set of u in U that are not in U - this is vacuously empty, and it is vacuously (and I am using the word deliberately, pun intended) a subset of U as well.

I have fixed the proof by using a collory that the empty set is a subset of everything.

But you think my proof is trivial. You are right. But for a beginner like me I want to make things rigorous even these basic things, after all it tricked me in thinking that the (proved) result was a contradiction.

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