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This is what happens when mathematicians get into arguments at dinner parties. The statement "f is not continuous at all the points of the closure of A" can mean either:
1. There exists at least one point where f is not continuous (woman yelling)
2. At every single point, f is not continuous (confused cat)
This is why mathematicians obsess over quantifiers like "for all" and "there exists." One misplaced word and suddenly your function goes from "slightly problematic" to "completely broken." And that's how you turn a simple calculus problem into a three-hour debate that ruins Thanksgiving.
