# [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 Previous message: [plt-scheme] The Lambda Calculus behind functional programming Next message: [plt-scheme] The Lambda Calculus behind functional programming Messages sorted by: [date] [thread] [subject] [author]

```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
> >
> >
> >
>
> _________________________________________________