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From: Marko Rauhamaa <marko@pacujo.net>
Newsgroups: comp.lang.python
Subject: Re: Suggestion: make sequence and map interfaces more similar
Date: Wed, 30 Mar 2016 14:44:00 +0300
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Jussi Piitulainen <jussi.piitulainen@helsinki.fi>:

> Manolo Martínez writes:
>> On 03/30/16 at 01:40pm, Jussi Piitulainen wrote:
>>> Yes, and most many-to-one mappings are *not* surjective.
>>
>> Well, I don't know about most, there are uncountably many surjective
>> and non-surjective many-to-one mappings :)
>
> Ok, safer to say that some many-to-one mappings are not surjective.
>
> I was thinking of finite sets, and not even really thinking. But even
> with infinite domain and infinite codomain, there can be uncountably
> many mappings without any of them being a surjection - just have the
> codomain be a larger infinity.

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.


Marko