On Jan 29, 2014, at 4:13 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> If I said a line is a "set of points" (with some further conditions) isn't tantamount to be "made up of points"? And that is more or less the standard view. All the stuff you need is in ZF along with, of course, proper definitions and development.
You would be using ?made up? in a very different context than the original poster I was addressing. You?re version of ?made up? wouldn?t lead you to then go on and start ?connecting? points together like a string of beads.
> I think perhaps I understand your feelings on where you'd like to go with this train of thought; you'd perhaps like "line" to be a very distinct "species" of mathematical object from "point", and that in fact may be closer to the way the ancient Greeks thought about it.
Not distinct species, just distinct circumstances. I was trying to help the original poster realize how easily one can confuse one?s own self if they are not careful with the extra baggage that labels bring with them. I want him to realize that his tendency to even want to know ?how many points are in a line" is the result of his notion that lines are ?made up? of points, which they are not. Not in the context he was thinking, like beads on a string.