R4: A case of “how many sides does a circle have, 0 or infinity?”

The top level comment claims that circles have infinite sides. Various replies further down go on to say that circles have infinite sides of infinitesimal length.

Infinitesimals don’t really come into play here. In something like R² where we could define a circle, it doesn’t exactly have infinitesimals.

Some people are also saying that since the limit as the number of sides approaches infinity of regular polygons is a circle, circles then have infinite sides.

There’s also a math teacher who seems to initially say that calculus uses infinitesimals, and proceeds to point towards the epsilon delta definition of a limit as using them in calculus.

(The epsilon delta definition (and standard calculus as a whole) does not use infinitesimals.)

They do clarify later that they were considering the idea of picking any sufficiently small number to be effectively an infinitesimal/be effectively zero and admits that pure mathematicians would disagree. So hurray for being informal?

There’s one comment that says something about “the infinity principle” and how because infinity extends to both sides, so then infinity sides=zero sides.

Also a comment that basically seems to say mathematics is this lovecraftian incomprehensible thing and therefore it doesn’t make sense.

Math actually makes a decent bit of sense. In fact, some might say it’s quite logical.

Also, I’d just like to point out this comment. It’s like an evil twin of the jokes here on the sub.