Thoughts on Infinity

[tcepsa]

If I'm remembering correctly, one of the generally accepted concepts in mathematics is that two lines in a plane will never intersect if and only if they are parallel. They go on forever without crossing. However, if they are out of parallel by the tiniest amount then at some point they must cross.

What point is that?

Comments

[tcepsa.livejournal.com]

Awesome, thanks for clarifying :) While it still kind of bends my brain to try to conceive of any two points directly across from each other on a circle as being the same point (very tricky to visualize, which is how I prefer to do things ;) I think that I have a better understanding of what that means.

To see whether I understand the idea behind the "line at infinity," it sounds like it is basically something that somebody came up with (a new axiom, because it wasn't derivable from the existing set of axioms?) to allow a different geometry (projective geometry) to exist which then makes it possible to address certain types of problems that weren't solveable (or were extremely messy) in the geometry defined by the previous set of axioms. Am I close? :)