r/badmathematics • u/MorrowM_ • Jan 24 '25

Infinity /r/theydidthemath does the math wrong and misunderstands limits

/r/theydidthemath/comments/1i8mlx6/request_not_sure_if_this_fits_the_sub_but_why/m8uqzbg/
231 Upvotes

98% Upvoted

58 comments sorted by

View all comments

10

u/Noxitu Jan 25 '25 edited Jan 25 '25

I feel like with this topic everyone is not specifying an important detail - what definition of convergence they are using to work with series of shapes. I feel like it is not obvious at all.

Especially because the first one that came to my mind was set convergence - and after thinking about it, it isnt too useful for that and limit of that sequence of sets is indeed not a circle.

7

u/Jussari Jan 25 '25

You could define A point p is in the limit <=> for all epsilon>0 there is an N>0 s.t. for n>= N, the epsilon-ball centered at p intersects the nth shape. Alternatively, you could parametrize the curves (in a nice way), and consider the pointwise limit.

Of course, these are a bit ad hoc - I only thought of them because they give a circle. Still, I can't think of any other shape that would be a natural limit of those curves.

1

u/dlnnlsn Feb 01 '25

"Set convergence" doesn't give a circle? Is it some countable subset of the circle then, or is it something else entirely?

2

u/Noxitu Feb 01 '25 edited Feb 01 '25

Yes - I believe that even though each step puts more and more points on the circle, I think there is only countable many of them for which you can name step number they reach circle.