From Newsgroup: sci.math



Xenocrates and line-reals

Well I'm reading C. Boyer's history of mathematics,
you know, a "The History ..." or the "A History, ...",
of mathematics, and he reminds that the idea of
the iota-values and line-reals or standard infinitesimals
is at least around since antiquity, then that besides
as atomism is like after Democritus, and the complete
ordered field is after Eudoxus, and Archimedes, then
when I say "Aristotle's continuum" as with regards to
line reals, it may as well be so to say "Xenocrates' ...",
not to be confused with Zenon.

Then, as with regards to those being usual objects
of mathematics in the mathematical universe, then
today simply disambiguating various models of
continuous domains as line-reals and field-reals
and signal-reals, of course is readily found in
the, "prior art", and not merely for partial soi-distant
Aristotleans that don't know the half of it.

Or, "Aristotle won't be fooled".

Of course there's lots of mathematics since
duBois-Reymond, Mirimanoff, and Skolem, say.

Yeah, infinity is "in" at least since the medieval
times since when the dunce cap was named for one
of the greater philosophers around since the founding
of the longest-running university in the world.


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