In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 1 Mai, 11:15, Dan <dan.ms.ch...@gmail.com> wrote: > > > It is necessary for Cantor's proof. Unless every digit exists on the > > > diagonal, the diagonal number is undefined in an undefined list. But > > > that is Cantor's claim: forall n : a_nn =/= d_n. > > > > It exists "as formula" , whether or not you know the formula . > > There are only countably many formulas. If all diagonals exist as > formulas, then all belong to a countable set.
But if there were only countably many reals, one only needs countably many formulas to find the nth digit of the nth real.
> > I told you the argument. Read it. Every rational has a number does not > mean all rationals have numbers.
Note that the only place where "for every" does not mean "without exception" is Wolkenmuekenheim. --