This seems like a pretty straightforward question (assuming I worded it well), but I've never been able to find an answer anywhere. So, in Euclidean geometry, a plane extends infinitely in all directions, meaning you can have things like
- two points any arbitrary finite distance apart
- infinite plane tilings
- etc
But spherical geometry, in my understanding of it, seems like it wouldn't be infinite in the same way, as going in one direction leads you back to the same place you started. You can imagine an infinite plane but not an infinite sphere. Also, there are some characteristics in spherical geometry that would only work on a finite geometry, such as any property relating to great circles (the existence of a great circle implies there is some "largest" circle, meaning the geometry cannot be infinite).
So (hoping this was worded clearly), would spherical geometry NOT be infinite? (such as, points cannot be any arbitrary distance apart, or there is some maximum distance two points can be apart?)