The intersection of any set A with the empty set (∅) is always the empty set, because no element can simultaneously be in A and in the empty set, making the condition 'X is in A and X is in ∅' always false, which defines the empty set.
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A⋂∅=∅ Proof Speedrun (ZFC Set Theory) #maths #proof #settheory #mathematics #math追加:
Well, if we simplify the intersection of A with the empty set, this is just the set of X such that X is in A and X is in the empty set, right? But now here's the thing, X is in the empty set, this is always false. So, whatever this is, something and false simplifies to false, okay? So, the set of X for which false is true is the empty set cuz there's no X that could make that true.
So, that's our first theorem.
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