[FOM] Intermediate value theorem and Euclid
pratt at cs.stanford.edu
Thu May 21 19:08:27 EDT 2009
On 5/20/2009 11:07 AM, Andre.Rodin at ens.fr wrote:
> From my part I don't think that such notions as
> *the right* notion of Euclidean plane (= what is the Euclidean plane
> "essentially") makes sense - althought I assume that there are more and less
> viable modernisations of this old mathematical notion.
Is there *the right* notion of abelian group? If not, why not? If so,
why that and not *the right* notion of Euclidean plane? And would your
answer change at all if "Euclidean plane" were replaced by "affine
space" (the abstraction obtained by Euler in the 18th century by
omitting the concepts of length and angle from Euclidean space)? That
is, is the Euclidean plane elusive in your view on account of having the
difficult notions of length and angle, or for some other reason?
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