On 4 Mai, 22:45, Virgil <vir...@ligriv.com> wrote: > In article > <06206984-5944-49e6-9ba6-9f795516c...@p14g2000vbn.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 4 Mai, 18:30, Dan <dan.ms.ch...@gmail.com> wrote: > > > > > Either they're both relevant to Cantor's argument, or they're both > > > > > irrelevant . > > > > > Cantor's argument > IS valid! > > > > Why should it be considered important under the definition of > > > equality? If they have at least one different digit , THEY'RE > > > DIFFERENT. > > > But there always only finitely many with at least one different digit > > whereas there are always infinitely many with none different digit. > > Name one!
A very good question. It is exactly this question that has turned modern mathematics into matheology.
For every n, I can name many larger numbers.
> Thus (reals countable) <==> (reals listable). > > But Cantor has shown that there is no complete list of real possible as > every listing of reals necessarily omits some reals.
And counterfactually he has assumed that there is a complete list of natural numbers. > > > My list is constructed such that all possible squences of digits 1 are > > already in the list. No longer sequence is possible (otherwise it > > would be in the list) and a shorter sequence cannot support Cantor's > > claim. > > Unless your list claims to list all reals, it has no effect on the > validity of the Cantor diagonal argument, which remains valid in spite > of it.
It is true: If the naturals are complete somewhere, the reals cannot be complete there. Alas this theorem is void since the naturals cannot be complete anywhere.