FOM: (no subject)

[Paul LEVY]

   After all, the initial year of someone  Joe Shipman
   is called FIRST year. 

Indeed it is, but that's a bad convention.

Here is the terminology I use, that I offer to anyone who might find it useful.  There are two conventions for ordinals:
"obaz" - ordinals begins at zero
"obao" - ordinals begin at one
My suggestion is to explicitly state which convention you are using.  
Examples:

The obaz first US president from the Bush family is George W. Bush.
The obao second US president from the Bush family is George W. Bush.

The obaz zeroth year of the obaz twentieth century was obaz 2000.
The obao first year of the obao twenty-first century was obao 2001.

The answer is the contents of cell obaz i in the array.
The answer is the contents of cell obao i+1 in the array.

The convention in English is obao with the exception of floors (in British English) and ages.   But of course it is obaz that is mathematically more natural. Stating "obaz" explicitly allosws you to use it without clashing with the conventions of English.

A related useful notation, where alpha is an ordinal, is to write $alpha for the set of ordinals < alpha, the canonical well-ordered set of order-type alpha.  Thus an array of size n is obaz-indexed by $n.  Of course in the usual ZF implementation, alpha and $alpha are the same, but that's just an implementation.



   The Pope is mathematically correct calling the 2000th year 
   year number 2000 anno domini. 

I think that the Pope would not regard the year 1 BCE as an annus domini.  So he would consider the year you're referring to be the obaz 1999th year, or year number obaz 1999 anno domini.  Since I consider obaz to be mathematically more natural, I don't agree with your statement.

Regards
Paul

http://www.pps.jussieu.fr/~levy