Re: how many RDF* triples?

Argh, I realize that I hit "reply" instead of "reply all", when
answering Peter's original message :-/

To sum up our exchange:

* the "infinitely nested" triples suggested by Peter should not, in my
opinion, be allowed, and I don't think Olaf's intention was to allow them;

* hence, I reverted the definition of RDF* triples to Olaf's original
definition (from the paper), which makes this restriction more explicit;

* with this restriction, I believe that the set of RDF* triples is
"only" countably infinite, as any RDF* triple can be serialized into a
(finite) string.

On 15/10/2020 09:06, Olaf Hartig wrote:
> Hi Pat,
>
> I understand the difference between uncountably infinite sets and countably 
> infinite sets, and I see that the set of all possible RDF* triples is 
> uncountably infinite. So, in that sense, yes, my comparison to literals was 
> imperfect as it was only about infinity without distinguishing between the 
> countable and uncountable variant.
>
> The main question is whether the uncountable infinity of all RDF* triples may 
> cause problems. I don't see how it may cause problems.
>
> Thanks,
> Olaf
>
>
> On onsdag 14 oktober 2020 kl. 16:27:03 CEST Patrick J Hayes wrote:
>> Hi Olaf
>>
>> Not quite the same issue with literals. There are countably many literals,
>> just as there are countably many possible IRIs and countably many RDF
>> graphs. But if Peter is correct, there are uncountably many RDF* triples.
>> An uncountable infinity is a lot more than a countable infinity.
>>
>> Pat
>>
>>> On Oct 14, 2020, at 8:00 AM, Olaf Hartig <olaf.hartig@liu.se> wrote:
>>>
>>> Hi Peter,
>>>
>>> Right, there is no bound on the nesting depth. However, I don't think that
>>> this may cause problems.
>>>
>>> By the way, the set of literals is infinite as well, so you have the same
>>> issue with RDF triples.
>>>
>>> Olaf
>>>
>>> On onsdag 14 oktober 2020 kl. 08:46:52 CEST Peter F. Patel-Schneider 
> wrote:
>>>> I was looking at https://w3c.github.io/rdf-star/ and got to wondering how
>>>> many RDF* triples are there?  It appears to me that there are an
>>>> uncountable number of RDF* triples because there is no axiom of
>>>> foundation
>>>> for RDF* triples.
>>>>
>>>> So the following is an RDF* triple:
>>>>
>>>> _:a :p << _:a :p << _:a :p << _:a :p ... >> >> >>
>>>>
>>>> So an RDF* triple could have an infinite number of elements and so there
>>>> is
>>>> an uncountable number of RDF* triples.
>>>>
>>>> Does this cause  any problems for RDF*?  That I am not sure of.
>>>>
>>>>
>>>> peter
>
>