> 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 tim

> 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).