Aluminium Holocene Holodeck Zoroaster wrote: > Zeno's paradox represents a dyscovery of "reals," > before any nomencature could be made, perhaps. >
I think Zeno's paradoxes, if taken seriously, tell us that the reals have to be defined geometrically, as points on the real line, as opposed to a purely algebraic definition. Euclidean geometry plays a vital role in the definition of reals that I have proposed in my paper <http://arxiv.org/abs/math.LO/0506475>. I think the Greeks would have been very pleased with this paper as it captures, to some extent, the Greek intuition that "completed" infinities (infinite sets) cannot exist and also proposes a resolution of Zeno's paradoxes which is different from that of classical real analysis.