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
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