On 23 Jun., 14:51, Sylvia Else <syl...@not.here.invalid> wrote:
> Cantor doesn't rely on being able to identify a last digit. He's just > saying that no matter how far down the list you look, you'll find that > the element at that point doesn't match the anti-diagonal.
That is wrong. Cantor uses the alleged "fact", that infinity can be completed, i.e., that that the infinite list can be finished. If he would only assume what you say, then the anti-diagonal could remain in the unknown part of the list. You know and appreciate that after *any* line number n there are infinitely many more lines?
> But you can't > even begin to formulate his proof if you can't identify the first > element of the list (and hence first digit of the anti-diagonal) either.
Isn't it enough, also in my case, to know that every antidiagonal has a first digit? In fact it has. Every antidiagonal is constructed from a list with a first line (that is the previous antidiagonal) and the remaining list. Every line has a finite number n. > > First and last are interchangeable, of course, but with your > construction above, you can't specify either the first or the last.
As I told you, my notation is only an abbreviation for the following definition: 1) Take a list L0 of all rational numbers. 2) Construct its antidiagonal A0. 3) Add it at position 0 to get (A0,L0) 4) Construct the antidiagonal A1. 5) and so on.
There occurs never a problem, because we know Hilberts hotel, don't we?