[FOM] Intermediate value theorem (and ASD)]]

Monroe Eskew meskew at math.uci.edu
Fri May 22 22:16:41 EDT 2009

On Wed, May 20, 2009 at 2:48 PM, Arnon Avron <aa at tau.ac.il> wrote:
> Talking about CALCULATING a Euclidean point makes sense
> only if you identify R^2 with the Euclidean plane. But
> this was exactly what I was questioning!

To clarify-- Do you see a problem in identifying the Euclidian plane
with Cartesian coordinates, or is it specifically the notion of the
powerset of the natural numbers that gives you trouble with R^2?  Let
E be the field of constructible numbers (in the Euclidian sense).
Would you identity the Euclidian plane with E^2?

> There is no sufficient evidence about Adam and Eve,
> but Euclid definitely did not identify curves
> with functions. You seem to forget the correct
> order of things. Curves are intuitive
> and come first. Differentiable
> functions are only (rather problematic) approximations.

Following the above theme, would it be OK to identity curves with
certain functions from E to E^2 (as in parameterized curves)?  Or
subsets of E^2 that admit a certain kind of parameterization?


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