Re: A model for the natural numbers

From: Anno Siegel (anno4000_at_lublin.zrz.tu-berlin.de)
Date: 07/25/04 

Date: 25 Jul 2004 18:41:51 GMT

Shmuel (Seymour J.) Metz <spamtrap@library.lspace.org.invalid> wrote in sci.math:
> In <cdr82i$ak8$1@mamenchi.zrz.TU-Berlin.DE>, on 07/23/2004
> at 02:41 PM, anno4000@lublin.zrz.tu-berlin.de (Anno Siegel) said:
>
> >It is somewhat unusual to include 0 in the naturals,
>
> No.

It was, for a long time. Times are a-changing, as I have acknowledged
elsewhere in the thread.

> >In fact, indexing from 0 instead of 1 has advantages
> >in some situations, as programmers know.
>
> Yes, as does indexing from 1 and indexing from -5. The fact that some
> languages index from a fixed value does not mean that there is
> anything either convenient or special about that value.

Practically, and historically, the values 0 and 1 *are* special,
as witnessed by the fact that they are the only fixed values ever
considered by main-stream languages. The trend is for newer languages
to have a fixed lower index 0. That is no coincidence.

For a practical example, the formulas that map an N-dimensional
array on a one-dimensional one are simplest when all arrays start
at zero. If there is a nonzero offset, you get to subtract it.

Anno

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