On 19 Jun., 08:12, Virgil <Vir...@home.esc> wrote:
> > No, for the fifth time now. The antidiagonal of a list of all > > computable real is not computable. How many more times would you like > > me to repeat this simple and mathematically obvious statement?
Please stop to repeat that. It is completely irrelevant. There is a list that contains all finite words. It includes all definable, constructible, computable numbers. > > There is, however, some question in my mind about the existence of a > list of all and ONLY computable reals.
Completely irrelevant. > > For countability of a set it is certainly sufficient to have a list > containing all its members even if that list is allowed to contain other > things as well.-
Correct. All numbers that somehow can be identified belong to a countable set.
Therefore Cantor either proves the uncountability of a countable set (by producing a diagonal number that can be identified) or he identifies an unidentifiable disgonal number. Both is a contradiction.
And I am very sorry for those "logicians" who try to escape this simple truth by sophisticated definitions that yield unidentifiable identities and other foolish notions.
A crank suffers from selective perception of reality, doesn't he?