# Dedekind's Axiom

You're quite right. I happened to notice your reply before I logged off. I didn't mean to just have the last word and run off, sorry if that was the impression. I was just explaining my comment about the paradoxicality of motion if spacetime is treated as series of points a la Zeno, which you'd asked about, and explaining that I was about to disappear from the discussion. I didn't want to go without warning. I shouldn't have mentioned Lynds. I'd like to discuss Zeno with you but will have to come back another time. Sorry if it seemed I was point scoring. My mistake.

Regards
Canute

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HallsofIvy
Homework Helper
Dedekind's axiom doesn't have anything to do with "motion" or Zeno. It is equivalent to the least upper bound property (or "monotone convergence", or the "Cauchy criterion" or the fact that the set of real numbers is connected (with the usual topology) or that every closed and bounded set of real numbers is compact (again with the usual topology).

mathwonk