python for loop

[Steven D'Aprano]

On Thu, 02 Apr 2009 04:23:32 +0000, John O'Hagan wrote:

> Beyond being part of a conventionally-ordered set of keys, what can an
> ordinality of zero actually mean? (That's a sincere question.)

In set theory, you start by defining the integers like this:

0 is the cardinality (size) of the empty set, the set with nothing in it.

1 is the cardinality of the set of empty sets, that is, the set 
containing nothing but the empty set.

2 is the cardinality of the set of the empty set plus the set of empty 
sets.

3 is the cardinality of the set containing the empty set, plus the set of 
empty sets, plus the set of (the empty set plus the set of empty sets).

And so forth, to infinity and beyond.

Or to put it another way:


0 = len( {} )
1 = len( {{}} )
2 = len( {{}, {{}}} )
3 = len( {{}, {{}}, {{}, {{}}} )
etc.

For non-infinite sets, you can treat ordinal numbers and cardinal numbers 
as more or less identical. So an ordinality of zero just means the number 
of elements of something that doesn't exist.

How that relates to whether indexing should start at one or zero, I have 
no idea.

Oh, and speaking of... I'm shocked, SHOCKED I say, that nobody has given 
that quote about the compromise of 0.5.


-- 
Steven