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7. Being precise.

The precision you hold yourself to through a rigorous approach to a problem is also very valuable and is the reason I think calculus is very important.




> The precision you hold yourself to through a rigorous approach to a problem is also very valuable and is the reason I think calculus is very important.

What property concerning precision does calculus have that doesn't hold for any topic in mathematics?


Infinity (and infinitesimals) is intuitively east to use but easy to misuse. Arithmetic isn't so easy to misuse.

Students usually see infinity for the first time in calculus (or maybe when working with infinite series)

These are the situations where we commonly see people being confident in their incorrect answers (which is worse than being unconfident and unable to get correct answers)

Difficulty wrangling infinity comes up a lot on Hacker News, even https://hn.algolia.com/?query=infinite%20series&sort=byPopul...


> Students usually see infinity for the first time in calculus (or maybe when working with infinite series)

Students also see groups or R-modules the first time in abstract algebra. So what.

> These are the situations where we commonly see people being confident in their incorrect answers (which is worse than being unconfident and unable to get correct answers)

> Difficulty wrangling infinity comes up a lot on Hacker News, even https://hn.algolia.com/?query=infinite%20series&sort=byPopul....

I rather the reason why "infinity" is misused so often, but, say, groups or R-modules, not so lies rather in the fact that too most math instructors too much to appeal to intuition in calculus, but not in abstract algebra. Thus mathematics should be taught in a much more abstract way where you are not misled by your bad intuition because you simply aren't able to formulate wrong thoughts in the abstract framework (that's why the abstractions and formalism was invented).


Indeed. The most precise I ever had to be was in my real analysis course. It seems agreed upon that all professors that teach it will be utterly pendantic about all proofs in that class. Which I agree with as a sort of gateway to graduate mathematics but man was it frustrating haha


Calculus doesn't have any true rigour/precision. That's why it's not analysis.


Maybe that would be an imprecise term then? ;)


I would argue that it sometimes gets in the way of the social life. Being able to stay very precise and keep in touch at the same time might be challenging for some.

Though, perhaps it's the other way and the overly precise (Asperger's syndrome?) people become mathematicians as opposed to them developing the precision?


I would also like to agree that precision can sometimes get in the way when confronted with so little of it in places of work or home.

I Live in a hundred year old home, have never seen a 90 degree angle on any of the walls and everything is a little off. Growing up learning fine wood working. My house has provided so many confounding moments.


Not all mathematicans are on the spectrum. When they have done studies the elevation in AQ is about 2 points, from mean 17 in population to 19. Autism starts at around 23 if I remember correctly.




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