# [plt-scheme] The Lambda Calculus behind functional programming

On Sat, Sep 01, 2007 at 02:53:58PM +0200, Jos Koot wrote:
>* ----- Original Message -----
*>* From: "Jens Axel Søgaard" <jensaxel at soegaard.net>
*>* To: "Jos Koot" <jos.koot at telefonica.net>
*>* Cc: "PLT Scheme" <plt-scheme at list.cs.brown.edu>
*>* Sent: Friday, August 31, 2007 8:38 PM
*>* Subject: Re: [plt-scheme] The Lambda Calculus behind functional programming
*>*
*>*
*>* >Jos Koot wrote:
*>* >>Would it make sense to present a formal mathematical definition of a real
*>* >>number on primary school as a starting point for elementary arithmetics?
*
formal??? probably not. Informal? maybe. The essence that has to be
conveyed is
You've got a real number when you can approximate it as precisely as
you want.
No need for Cauchy sequences.
You can even discuss what's not a real number then -- such as physical
measurements, which are ultimately limited by the precision of our
measuring instruments.
>* >
*>* >That depends on how formal you want to be. One way to formalize
*>* >real numbers is to consider equivalence classes of Cauchy sequences,
*>* >but that seems a little extreme in primary school :-)
*>*
*>* Exactly.
*>*
*>* >But examining the definition of fractions might be an option?
*>*
*>* And on high school, may be cycling versus non cycling decimal expansions.
*>* Yes, I assume so.
*>* But nevertheless you wont't be telling the whole story. Of course not. You
*>* cannot tell the whole story at once.
*>* You have to dose it in small portions.
*>* Jos koot
*>*
*>* >--
*>* >Jens Axel Søgaard
*>* >
*>* >
*>* >
*>*
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