[adenadel]

This is not true. The usual calculus that people learn (and usually learn with rigor in a real analysis course) does not touch infinitesimals.

The approach via infinitesimals is even called "nonstandard analysis".

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

[jyounker]

You're absolutely right. I was going for a different concept. See explanation above. I should stop writing after 02:00.