Re: Euclidean Geometry in Schools

Jean-Claude Arbaut a écrit : 


On 26/06/2005 12:42, William Elliot wrote:


From: Jean-Claude Arbaut <jean-claude.arbaut@xxxxxxxxxxx>

Herman Rubin wrote: 

The teachers seem unable to unlearn the idea that numbers are
strings of decimal digits, to be manipulated.  They cannot
understand that the representation by decimal digits is a
derived representation and a convenience, not at all basic.

But real numbers *are* (infinite) strings of digits! 


Sigh. "Real numbers may be represented as finite or infinite strings of
digits, with sometimes a decimal point". I answered in another post that the
correct characterization is given by properties. Basically, all Q
properties, plus "every majorized subset of R has a sup".
And they should be constructed from Q with Cauchy series or Dedekind cuts. I
like the latter, but Cauchy series can be generalized, so the idea seems
better.


Cuts can be generalized too : see Conway's surreal numbers
.

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