> Actually, having an infinity at the end of > every line on the complex plane just gives > you a simple disc. Er, judging from the rest of your comment yo

> Actually, having an infinity at the end of > every line on the complex plane just gives > you a simple disc. Er, judging from the rest of your comment you must simply have misunderstood me. For every line through 0 in the complex plane, take a point and define it to be at both ends of the line. That is doing as you say, associating antipodal points. And I do do calculus (well, equivalent procedures) on such objects. It's clear from your comments that you know about these things - trust me that I do as well. So we're agreed that the concept of infinite sized sets and the concept of "points at infinity" are different, and for teaching about "infinity" it might be useful to separate them explicitly. Interesting observation. Thanks.