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I don't like clickbait... The article starts to suggest that calculus is hard to reason about and "irrational". In the end all it is really saying is that calcu

I don't like clickbait... The article starts to suggest that calculus is hard to reason about and "irrational". In the end all it is really saying is that calculus requires irrational numbers, well doh! And guess what, you even need complex numbers. And the question is not about "shopping" numbers, there is a history to all of that. If you want something universal, use complex numbers. Try to teach that to a pre-schooler and you will find that you might wanna start with something simpler.

ColinWright 7y ago
> ... In the end all it is really saying is that calculus requires irrational numbers, well doh! 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.
JackFr 7y ago
> And guess what, you even need complex numbers. 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-Mathematics/dp/0486428753/ref=asc_df_0486428753/?tag=hyprod-20&linkCode=df0&hvadid=312168166316&hvpos=1o1&hvnetw=g&hvrand=1608085467130596869&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9067609&hvtargid=pla-514661979117&psc=1 https://www.amazon.com/Counterexamples-Analysis-Dover-Books-... (Pdf version) https://pdfs.semanticscholar.org/a4e7/eb352e4c44bf75d8fabaf7594494151cb322.pdf https://pdfs.semanticscholar.org/a4e7/eb352e4c44bf75d8fabaf7...
nerdponx 7y ago
Consider the author and the target audience. Is it clickbait, or a pun?
ozim 7y ago
I'd say it is quite smart clickbait and the one I can live with. If I have to compare with "Celeb X did so outrageous thing!!!!" which turns out X parked on a spot for disabled or whatever.
vharuck 7y ago
>And guess what, you even need complex numbers. 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
yura 7y ago
"I don't like clickbait... The article starts to suggest that calculus is hard to reason about and "irrational". In the end all it is really saying is that calculus requires irrational numbers, well doh!" 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.

ColinWright 7y ago

> ... In the end all it is really saying is that calculus requires irrational numbers, well doh! 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.

JackFr 7y ago

> And guess what, you even need complex numbers. 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-Mathematics/dp/0486428753/ref=asc_df_0486428753/?tag=hyprod-20&linkCode=df0&hvadid=312168166316&hvpos=1o1&hvnetw=g&hvrand=1608085467130596869&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9067609&hvtargid=pla-514661979117&psc=1 https://www.amazon.com/Counterexamples-Analysis-Dover-Books-... (Pdf version) https://pdfs.semanticscholar.org/a4e7/eb352e4c44bf75d8fabaf7594494151cb322.pdf https://pdfs.semanticscholar.org/a4e7/eb352e4c44bf75d8fabaf7...

nerdponx 7y ago

Consider the author and the target audience. Is it clickbait, or a pun?

ozim 7y ago

I'd say it is quite smart clickbait and the one I can live with. If I have to compare with "Celeb X did so outrageous thing!!!!" which turns out X parked on a spot for disabled or whatever.

vharuck 7y ago

>And guess what, you even need complex numbers. 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

yura 7y ago

"I don't like clickbait... The article starts to suggest that calculus is hard to reason about and "irrational". In the end all it is really saying is that calculus requires irrational numbers, well doh!" 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.