Hallo Martin,
Du schriebst am Wed, 11 Apr 2012 09:09:42 +0200:
> BTW, I don't like the one-based FPC recno, I think it should be
> zero-based. What do you think?
That's the distinction between _counting_ and _numbering_.
Do you count "0, 1, 2..."? Probabely not.
How do you number things?
Doesn't matter at all, because here, the numbers are just labels. Odered
labels, usually, but just labels. You could use any other set of symbols
having an oder relation, like letters of the alphabet, or the number names
("One, two, three...").
There's even a mathematical concept for each of these:
counting numbers are called "cardinal", while numbering numbers (;) are
called "ordinal".
Calculating is only defined for cardinal numbers, you can add, subtract or
multiply them (division is a special case here, because division cannot be
defined wholly within the cardinal number's space).
With ordinal numbers, you only have distance between them.
Usually, this isn't recognized, as one doesn't commonly attempt to multiply,
e.g., record numbers or array indices, or even add them together.
Subtracting two ordinal numbers produces _not_ an ordinal, but a cardinal,
giving the distance between the two. Distance can be positive or negative,
because ordinals are ordered - you can always tell whether one comes
"before" the other, is "smaller" by means of the ordering relation.
An implementation of ordinal data are Pascal's enumerations, a "typical"
use are array indices - which, in Pascal, are implemented such that there
is a starting value and a sequence defined, where the starting value can be
anything allowable for the index value. You can also use enumerations as
indices.
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