What is the Intersection of the Null Set? (Set Theory Proof)

A video looking proving that the intersection of the null set is the universal class: V=⋂∅.

This series covers the basics of set theory and higher order logic. In this month we are looking at the Operations and Relations of Sets. This month includes unions, intersections, differences, power sets, Cartesian products, functions, ordered pairs and more! We are also looking at the fifth and sixth axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at Peano Arithmetic. (#SetTheory #Logic)

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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

[ebyronnelson]

This proof all makes sense to me (I was able to do the first half pretty easily on my own and then got the second half after the reminder here of the class definition). However, intuitively, the idea that the intersection of the null set, which has no members, is the same as the universal class doesn't make sense to me. It almost seems like set theory's version of dividing by zero, except here we are allowed to say that 1/0 = ∞. How can every set be a shared member of nothing?

[paulapiqueras]

Addition has never made sense to me (I have to say i haven't studied this for long). Addition states that you could disjunct anything to a tautation, and the result would also remain a tautation. However, that means you could make any implication you want. For example, we could do t∈V v t∈∩∅　≫　t∉V⊃t∈∩∅, in other words, anything which is not a set is in the intersection of the null set. This would mean that also any class is in the ∩∅, and that the ∩∅ would be "bigger" than the universe. Do you find any flaws in my conclusion?

[loopy]

I have no idea what you're on about