You're absolutely right. I don't know what I was thinking when I wrote this last night. I meant to say that formal treatments are based around being able to fi

You're absolutely right. I don't know what I was thinking when I wrote this last night. I meant to say that formal treatments are based around being able to find arbitrarily small neighborhoods around a point, and that this only works when you have something the size of the reals, for which you can find a real-sized space between any two points. It's this infinite self-similarity at any arbitrarily small scale that is at the heart of calculus.