I would say that I am not a specialist of categories. There are many
enhancements introduced by #10963. In particular, when you create a
category you can do Sets().Finite() or Sets().Infinite() in a cleaner
way. I guess we would like something like InfiniteCountable() (as a
synonym of Infinite()) and InfiniteUncoutable() ? It might be tricky
as for example EnumeratedSets().InfiniteUncountable() should not
exist...

the part of category for InfiniteUncoutable() might provide
 - the good infinity for cardinality() in order that
{{{Words(2).cardinality() ==  NN.cardinality()}}} is False.
 - the error for __iter__

2013/12/3, Nathann Cohen <nathann.co...@gmail.com>:
> Yoooooooooo !
>
>> RR in Sage *is* countable and *is not* the set of real numbers.
>> Nevertheless it is not iterable (I do not know why).
>
> sage: RealField()
> Real Field with 53 bits of precision
>
> Oh. Right. Precision.
> :-P
>
>> Currently there is only finite versus infinite for sets. I agree with
>> you, it would be nice to have a category to deal with by essence non
>> iterable sets such as Words(2).
>
> Oh. So there is none ? Do you know how to create it ? (I still know
> nothing about categories).
> What could we put inside ? This exception for __iter__, what else ?
>
> Nathann
>
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