this post was submitted on 20 Oct 2024
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This isn't a rigorous mathematic proof that would prove that it holds true in every case. You aren't wrong, but this is a colloquial definition of proof, not a mathematical proof.
so... maybe its not worth proving then.
Oh trust me, I believe you. Especially using modern set theory and not the Principia Mathematica.
Only works for a smooth curve with a neighbourhood around it. I think you need the transverse regular theorem or something.