On 13 Apr., 06:47, "AMiews" <inva...@invalid.com> wrote:
> >every d_n of a numerical Cantor-list is the last digit of a > >terminating decimal. > >Never, do you understand, never anybody has seen or used a d_n that > >does not belong to a terminating decimal. > > you seem confused by standard math notation here. Irrationals no one has > seen the end.
But you believe in its existence nevertheless? There is no end and there is no "all", because every scientific use of "all" would include to find all. And that includes to prove that all have been found. And that includes that a last one has been confirmed. > > >Therefore Cantor proves that the countable set of rationals is > >uncountable. > > that is what you say, but study up on common math notation first. > Common math notation says that the digit d_n has the place number n and belongs to a finite sequence of digits. Cantor's method is incapable of dealing wth irrational numbers, because nobody can use them other than by a finite formula. Alas there are only countably many finite formulas.
Also the set of all defined Cantor-lists and all possible diagonals belongs to the countable set of finite definitions. So Cantor proves that this countable set is uncountable. Not a contradiction of course. Beware of such devilry in matheology!