"WM" <email@example.com> wrote in message news:firstname.lastname@example.org... > On 8 Jul., 19:12, "LudovicoVan" <ju...@diegidio.name> wrote: >> "WM" <mueck...@rz.fh-augsburg.de> wrote in message >> news:email@example.com... >> > On 8 Jul., 19:01, "LudovicoVan" <ju...@diegidio.name> wrote: >> >> "WM" <mueck...@rz.fh-augsburg.de> wrote in message >> >>news:firstname.lastname@example.org... >> >> >> > Ask yourself the question: What should remain inside? >> >> >> I think you miss the point: I was asking for a valid proof. >> >> > How can an invalid theory generate a valid proof? >> >> Are you kidding me? Where did you show that set theory is invalid? >> Again: >> either you show a *valid* proof in the language of set theory that the >> vase >> ends up empty (hence showing set theory unsound), > > What do you understand by language of set theory? It is a nonsense > standpoint (that could be due to MoeBlee) to claim that set theory > needs a certain language. > > If there is a bijection between every element m of a set M and every > natural number, then the set M is exhausted. And in my example that is > the case. > > If every natural number m leaves the urn, then there cannot any > natural number remain in the urn. Otherwise set theory was > inconsistent too.
There are in fact no natural numbers left in the urn. That is not to say, and it would be incongruent to say, that the urn is empty. A source of confusion with this problem is to mistake the balls for their labels.
>> or the Ross-Littlewood >> paradox is just a mistake on the part of some mathematicians. > > The problem is neither underspecified nor ill-defined. Completed > infinity is nonsense. Parallel: The "sum" 1/2 + 1/4 + 1/8 + ... is not > 1. 1 is only the limit. There is no infinite sum, because that would > require an end-signal.
Nonsense is to use limits and still claim that limits make no sense. Nonsense is to deny that Achilles reaches the tortoise or that an arrow reaches its target.