# [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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