you are quoting my quotation of Miles Mathis. i don’t endorse his theories, and even he is not really saying “calculus is straight-up wrong”. his argument is apparently more subtle than that, though i have not yet understood it.
I assume you say that because “infinity” and “infinitesimals” are only concepts and not actually numbers, or anything that exists in the real world. I’m fine with that. But how is this a problem with calculus?
The very definition of a derivative contains a limit, so if limits are nonsense then the definition is flawed at its foundation. Anyway, very smart people have had problems with the calculus from its very beginning (for instance, George Berkeley had a pretty interesting critique).
“What Berkley criticized in The Analyst as far as I can see is what later became nonstandard analysis. Which I dislike, but is valid and rigorous.”
Or instead of navel-gazing, you can be like the great Leibniz and use infinitesimals with aplomb. While Leibniz and Newton provided tremendous advances in mathematics and physics, Berkeley’s pedantic hand-wringing was all for nought: “non-standard analysis can be seen as a belated vindication of Leibniz’s mathematical reasoning.” - http://en.wikipedia.org/wiki/Gottfried_Leibniz