That's not true, and that is the point. To prove the main theorems of calculus, you don't need complex numbers, but you do need irrationals.
When you first learn calculus, you do one or two epsilon-delta proofs, and then your teacher gets a little hand wavy about limits and you move on to the real work of derivatives and integrals, cause the limits stuff intuitively makes sense. When you continue on in Real Analysis or Topology of the Real Line, you discover that your intuition lied to you, and concepts like open and closed sets and intersections and accumulation points are important and are in general non-obvious.
Counterexamples In Analysis
https://www.amazon.com/Counterexamples-Analysis-Dover-Books-...
(Pdf version) https://pdfs.semanticscholar.org/a4e7/eb352e4c44bf75d8fabaf7...
That's really not the point, it really isn't. In the middle it says:
"The theorems of the calculus that work for the reals but fail for the rationals, despite the very different claims they make, are all equivalent to each other!"
There's something quite deep going on with the reals, and it may be that you don't realise it, that you do realise it and don't care, or whatever, but it's not as simple as you seem to be implying.
Agreed. I did not want to click it, because I knew the author could not prove that Calculus made no sense. But due to the high amount of upvotes, I wanted to see just what were his arguments. The title turned out to be just a pun; which also happens to be clickbait-y, though I don't think that was an accident. As the author said, nothing in the post is particularly deep or surprising to anyone who has taken a course on real analysis, or even Calculus with some amount of rigor (which is unfortunately getting increasingly rare). This kind of subtle clickbait is, IMO, even more harmful than the obvious kind: whereas one can simply ignore the latter, in this particular case I couldn't figure out whether the title was a clickbait or not, and I had to waste time reading it to find out it's not what I thought it was, and it's not what I was interested in reading.
Complex analysis was definitely interesting. I hope there was an award for whomever figured out the easiest way to integrate some real-to-real functions was by side-stepping into imaginary numbers