system
Given the following post, respond as if you're commenting on Reddit:
human
Does a perfect sphere have zero, one, or infinite faces?

Does a face have to be flat?  Then it would be zero, right?  If not, I would think the answer is one.  But if you had an approximation of a sphere, like a polygon but 3d, the more faces you added, the closer to a sphere it would be.  So along that line of thinking, infinity faces would yield a prefect sphere.  Help.  Thanks!

EDIT: Thank you everyone for your answers!  Very interesting!
gpt
It doesn't have any faces (i.e., 0) because a face is a part of a plane, therefore flat. Infinite faces would yield a perfect sphere--with faces of zero area--but infinity is not a number, so you can't really get there. If you've the mathematical interest to pursue it further, the concept you're brushing up against is that of a "limit", which is the magic glue that holds the Calculus together.

(B.S., Math '93. Lots of folks who know a lot more will answer more precisely and rigorously.)