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Comment by esmi | Hacker News Reader

> I go on to claim, though I'm more unsure of this, that the real numbers are not even the only way to make calculus work.

That claim is certainly true. The proof is that calculus (Analysis) exists for the complex number system too. Although I don’t think that’s what you meant and I doubt the complex number system is “more intuitive.” Just out of curiosity, have you heard of real analysis? How do you define calculus?

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Take a look at nonstandard calculus:

https://en.wikipedia.org/wiki/Nonstandard_calculus

It is based on the hyperreal numbers:

https://en.wikipedia.org/wiki/Hyperreal_number

Practically speaking, I don't think it buys you anything over traditional calculus/analysis. It's just pointing out that there are alternative approaches to formalizing calculus.

A Riemann integral in complex analysis uses the same definitions as one in real analysis. Derivatives ditto. In the thread we're comparing real analysis to nonstandard analysis.

I'm eager to be corrected if you can tell me something I said that's wrong. I'm not interested in gradually upping the ante with you until it's clear who really has more math background.

I didn’t really see anything wrong in the thread but you use words like “calculus” and I honestly don’t know exactly what you mean. Do you mean the plug and chug methods often taught in high school? Or do you mean the application of a set of theorems derived from the axioms of a given system of numbers? If you mean the former then perhaps we can clear up some misconceptions which are clarified by the latter.

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