## [REBOL] Re: Natural numbers

### From: joel:neely:fedex at: 4-Jul-2001 7:00

Hi again, Alek,
Alekk wrote:

> I think You have gone to far. ;)
> It is not my opinion - natural numbers are with us from very
> past (fact is that there was not number 1 in those numbers
> in greek mathematic). When You say that natural numbers
> starts with 0 because one man (i agree - great) in XX century
>

XIX, actually. (The axioms date from 1891. ;-)

> made axioms about it - it sounds like "there was no world
> before 1796".
> When is 0 or not in natural numbers, is matter of context.
>

As you correctly point out, the ancient Greeks didn't even
consider 1 as a "number". Many of them also believed that
the world was flat, that the sun rode on a chariot, and that
air, earth, fire, and water were the basic physical elements.
It hardly seems fair to restrict our science or mathematics
to what they understood... :-}
Perhaps I didn't express my point sufficiently clearly (if
so I apologize):
"natural number" is a mathematical concept, and the
standard model in mathematics is Peano's axioms.
In the same sense as the statement:
"quark" is a physical concept, and the standard model in
physics (quantumelectrodynamics IIRC) uses that concept.
In neither case do we limit ourselves to the boundaries of
knowledge of the past.
-jn-
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joel'dot'neely'at'fedex'dot'com