[plt-scheme] The Lambda Calculus behind functional programming

((((lambda(x)((((((x x)x)x)x)x)x))
   (lambda(x)(lambda(y)(x(x y)))))
  (lambda(x)(write x)x))
 'greeting)
----- Original Message ----- 
From: <hendrik at topoi.pooq.com>
To: <plt-scheme at list.cs.brown.edu>
Sent: Saturday, September 01, 2007 10:14 PM
Subject: Re: [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.


Given an arbitrary real number you can approximate it
as precisely as you want by means of fractions
(unless "as precisely as you want" includes approximation-approximated=0)
Therefore I do not understand what you mean.

Jos Koot

>  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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