[plt-scheme] The Lambda Calculus behind functional programming

From: hendrik at topoi.pooq.com (hendrik at topoi.pooq.com)
Date: Sat Sep 1 16:14:49 EDT 2007

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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