Combining infinite ranges

[Andrei Alexandrescu]

On 05/31/2010 08:54 PM, Andrei Alexandrescu wrote:
> On 05/31/2010 08:07 PM, Simen kjaeraas wrote:
>> Andrei Alexandrescu <SeeWebsiteForEmail at erdani.org> wrote:
>>
>>> Yah, there's no argument that infinite ranges must be allowed by a
>>> n-way cross-product. It reminds one of Cantor's diagonalization, just
>>> in several dimensions. Shouldn't be very difficult, but it only works
>>> if all ranges except one are forward ranges (one can be an input range).
>>
>> Might I coerce you into indulging some more detail on this idea? I'm
>> afraid my knowledge of the diagonal method is sadly lacking, and some
>> reading on the subject did not give me satisfactory understanding of
>> its application in the discussed problem.
>>
>> Way I thought of doing it is save the highest position this far of each
>> range, then in popFront see if we're past it. If we are, reset this
>> range, and pop from the next range up, recursively.
>
> I thought about this some more, and it's more difficult and more
> interesting than I thought.
>
> Cantor enumerated rational numbers the following way: first come all
> fractions that have numerator + denominator = 1. That's only one
> rational number, 1/1. Then come all fractions that have num + denom = 2.
> That gives 1/2 and 2/1. Then come all fractions that have num + denom =
> 3, and so on.

I'm off by one there, but you got the idea :o).

Andrei