[plt-scheme] Re: Natural numbers

On Thu, 12 Mar 2009 04:06:12 +0100, "Jos Koot"
<jos.koot at telefonica.net> wrote:

> On Mar 11, 2009, at 8:33 PM, Norman Gray wrote:
>
>> In maths, the term "the natural numbers" refers specifically to the  set 
>> of positive integers (see for example [1]), and not to any set 
>> isomorphic to that.  Thus it does not depend on what you or I may  or may 
>> not find natural, and its meaning is not really a matter for  dispute. 
>> Anyone who refers, in any sort of semi-formal context, to  "the natural 
>> numbers" as meaning anything other than {n in Z : n >  0} is being 
>> quixotic.
>
> I was brought up with "the natural numbers" meaning {n in Z : n >=  0}. 
> In both my dissertation and my advisor's, and many of the
>
>Usually the letter 'Z;' is used for the set of complex numbers (Q for 
>rational numbers and N for natural numbers). If n is a complex number, then 
>what is the meaning of 'n>=0'?
>You confuse me.

No.  Z usually denotes the set of integers; C usually denotes the set
of complex numbers; z can denote a specific complex number (see "The
dictionary of basic mathematical notations in Mizar" at
http://markun.cs.shinshu-u.ac.jp/kiso/projects/proofchecker/mizar/mizardictionary1.htm).

In "{n in Z : n >=  0}," the 'n' denotes an integer in Z, the set of
integers.

Incidentally, according to the above-mentioned reference, 

>1.       N  the set of natural numbers with 0  [mizar]  NAT (numbers:funcnod 1); omega  (ordinal2:def 5)
>
>[usage]  0 in NAT  [0 is an element of N.]

"0 is an element of N."  However, according to other references, 0 may
not be an element of N, too, so this topic is open to interpretation.

-- Benjamin L. Russell
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