Subject: categories: Re: RFN (Request for Notation)

From: Paul Levy <[email-masked]>
Date: Wed, 29 Nov 2000 18:02:27 -0500 (EST)

> 
> (3) I badly need a good name for the sets
>         Nat_k = {n \in Nat | n < k }
>     These are widely used and I am surprised that
>     there is no satisfactory name in wide-spread use.
>       These are NOT the sets Z_k = Z mod k,
>     although the Nat_k form a system of distinct,
>     canonical representatives for the Z_k.
>       These are the set of array indices in computer
>     languages such as C and SML.  In this use, the
>     Nat_k have nothing whatsoever to do with Z_k
>     and I certainly do not want to confuse the students!
> 

I agree that there is a need for a standard name, and that Nat_k would 
be a confusing name.  I have been calling
this set $k for some time but I am happy to change my macro if there
is some other accepted name or if $ has some other mathematical meaning. 
More generally, if k is an ordinal, one writes $k for the set of
ordinals less than k, the canonical well-ordered set of order-type k.
(The traditional ZF definition of ordinal makes k equal to $k, but
that is just an implementation.)   

A similarly useful terminology for arrays and the like is
"obaz", which indicates the use of the "ordinals begin at zero"
convention.  Thus you can refer to the cell with index 7 in your array 
 as the obaz 7th cell instead of as the 8th cell.
You can't call it the 7th cell, without qualification, because in
English the obao ("ordinals begin at one") convention is the 
established default, unfortunately.

As an example, today is the obaz 28th day of the obaz 10th month of the
year obaz 1999, which is the final year of the obaz 19th century and not 
the obaz zeroth year of the obaz 20th century as many obaoists mistakenly
believe.   Though I'm hardly the zeroth person to point this out (obaz).

Warning: this usage may alienate the less tolerant of your friends.

Regards
Paul

-- 
Paul Blain Levy
Computer Science Department, Boston University
http://www.dcs.qmw.ac.uk/~pbl/
If language were arbitrary, it wouldn't be interesting.