On Thu, 2009-04-02 at 06:28 +0000, Steven D'Aprano wrote:
> In set theory, you start by defining the integers like this:
<snip>
>
> 0 = len( {} )
> 1 = len( {{}} )
> 2 = len( {{}, {{}}} )
> 3 = len( {{}, {{}}, {{}, {{}}} )
> etc.
not quite len() - surely you mean something like "any object along with
an algebra in which the left hand side is equivalent to the right in the
algebra of set theory?" - at least for ordinals.
The cardinal is then (for finite numbers) the length of that.
Or, in a pythonic sense (taking 0,1,2,... to be variable names):
0 = set()
1 = set(0)
2 = set(1,0)
3 = set(2,1,0)
3 = set(3,2,1,0)
etc.
> How that relates to whether indexing should start at one or zero, I
> have
> no idea.
so in this sense, range(n) is actually very close to the ordinal value
of 0 (except for being a list and not a set - but it's not in 3.0)
i.e. range(n) returns something very similar to the ordinal "n", and
with cardinality n. That seems very sensible to me.
> Oh, and speaking of... I'm shocked, SHOCKED I say, that nobody has
> given that quote about the compromise of 0.5.
"God made the integers, all else is the work of man" - Leopold Kronecker
...holding myself back from complaining about integer division in Py3K
when the philosophical question of whether irrational numbers even exist
(in a physics sense) is fairly open.
Tim W
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