In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 11 Apr., 21:41, Virgil <vir...@ligriv.com> wrote: > > > > > > In a Cantor list the argument can be written: > > > For every n: (d_1, ..., d_n) differs from every entry (qk1, ..., qkn) > > > with k =< n, i.e., i.e., every entry of the first n lines. That is > > > exactly Cantor's argument, not more and not less. > > > > That is WM's argument. > > Cantor's was much simpler: > > > Given an infinite list of binary sequences, there is a binary sequnce > > that differs from the nth sequence in that list at its nth term. > > What is the difference to my argument? Cantor's is (1) easy to understand and (2) relevant to the issue of whether the set of all binary sequnces is countable or not.
WM's is neiher. > > > > > > > > > In a list containing all rational numbers > > > > Cantor's original argument is about binary sequences, > > In a list containing all binary sequences holds exactly the same. > > > and until WM can > > falsify that one, > > Let the list conatin all binary sequences q_k.
That is assuming something that is false, so that any result follows,
> The counter-argument can be written: > For every n: (d_1, ..., d_n) does not differ from infinitely many > entries (qk1, ..., qkn) with k > n.
Does "(qk1, ..., qkn)" mean "(q_k1, ..., q_kn)" or "(qk_1, ..., qk_n)" or something else entirely?