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> 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

by wolfgke 10y ago

> 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?

eximius 10y ago
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
srtjstjsj 10y ago
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=byPopularity&prefix=false&page=0&dateRange=all&type=comment https://hn.algolia.com/?query=infinite%20series&sort=byPopul...
- wolfgke 10y ago
  > 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.. 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).

by wolfgke 10y ago

eximius 10y ago

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

srtjstjsj 10y ago

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=byPopularity&prefix=false&page=0&dateRange=all&type=comment https://hn.algolia.com/?query=infinite%20series&sort=byPopul...

wolfgke 10y ago
> 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.. 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).