Re: Thinking about MINUS

From: DBMS_Plumber <paul_geoffrey_brown_at_yahoo.com>
Date: 8 Jan 2007 10:59:45 -0800
Message-ID: <1168282785.333279.128190@q40g2000cwq.googlegroups.com>

Aloha Kakuikanu wrote:
> DBMS_Plumber wrote:
> > Marshall wrote:
> > > Even if we consider a system consisting only of the natural numbers,
> > > zero, successor and predecessor, we have to wrestle with the question
> > > of what the predecessor of zero is.
> >
> > Zero is not an element of the domain of natural numbers.
>
> It certainly is.

From: http://en.wikipedia.org/wiki/Natural_number "The natural numbers presumably had their origins in the words used to count things, beginning with the number one."

From: http://mathworld.wolfram.com/NaturalNumber.html "A positive integer 1, 2, 3, ... (Sloane's A000027). The set of natural numbers is denoted N."

>From Wordnet:

"the number 1 and any other number obtained by adding 1 to it repeatedly"

To be fair, what's confusing is that Peano axioms are often set down starting with '0 as a natural number', which (IIRC) simplifies some of the subsequent exposition. But this is a notational, not a logical, difference. Intuitively, the first 'symbol' (1, or 0, or |) is an anchor with special properties (see axiom # 3).

Also, you will note that Peano nowhere mentions the concept of a 'predecessor'. Induction points one way. Received on Mon Jan 08 2007 - 12:59:45 CST