Gabriel can fuck himself in the ass with his own horn

Why do you gotta post this at 1 am, my brain hasn't woke up. I wish we disn't need sleep.

>>8508111
>supposedly the converse, a solid of revolution with finite surface area but infinite volume, is impossible

Imagine an infinite cube with a finite unit cube missing. The surface area is 6

This is sort of right. You've just defined the surface area of the sphere as a plane with two arbitrary sides so that you can deny one is "inside" and one is "outside". But then any arbitrary enclosed area can be said to "contain" infinite volume.

>>8508117
that's basically the whole point of this thread

gg

>>8508120
Yeah but he didn't go on and on about it like op did.

By that logic, 3-space itself is a solid of revolution -- of 2-space about any line within it -- and said solid of revolution has a surface area of 0, because it has no surface at all.

The only exception would be if we were working in a geometry defined by a one point compactification of the reals. If there's a point at infinity, then it makes sense to say 3-space is in fact bound by at least one surface, at the same distance from the origin as the point at infinity is from 0. Its surface area is then necessarily infinite.

UNLESS!!

Wait a minute. The one point compactification of the reals is called ONE point for a REASON. If our geometry is based thusly, then infinity is THE SAME POINT along all three axes, and negative infinity along each of them is ALSO that same point. So the surface of 3-space isn't an infinite 2-manifold. It's a point.

Therefore, its surface area is 0 either way.