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From: Manolo =?iso-8859-1?Q?Mart=EDnez?= <manolo@austrohungaro.com>
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Subject: Re: Suggestion: make sequence and map interfaces more similar
Date: Wed, 30 Mar 2016 15:13:06 +0200
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On 03/30/16 at 03:55pm, Marko Rauhamaa wrote:
> Manolo Martínez <manolo@austrohungaro.com>:
> 
> > On 03/30/16 at 02:44pm, Marko Rauhamaa wrote:
> >> I don't even know if you can say much about the cardinality (or
> >> countability) of mappings. The general set of mappings can't exist.
> >> The *class* of mappings does exist in some set theories, but I don't
> >> believe classes have cardinality.
> >
> > I guess I was thinking of the cardinality of the set of tuples with
> > members of the domain in the first member and their image in the
> > second.
> 
> If you fix the domain and codomain, then we can discuss cardinality
> again, but the answer depends on the domain and codomain. For example,
> if the domain is the empty set, there exists precisely one function. And
> if the codomain is the empty set as well, that function is a bijection.

Yeah, what I said and you quote above is wrong: I was thinking of the
cardinality of the set of those sets of tuples. This seems like the kind
of thing that would result in set-theoretic paradoxes, so yes, you are
probably right that the cardinality of mappings is not well defined.

Manolo