On 2010-06-18, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Wrong. Cantor's diagonal construction explicitly forms a Real not on > that list, and the Cantorm diagonal number is obviously constructibe > if every item in the list is constructible.
You are now mixing up "constructible" with "computable", getting yourself even more confused.
It is certainly possible to have a list of computable numbers that is not computable itself. For example: Chaitin's Omega is not computable. Define a list L such that the n'th entry on the list consists of all 1's if the n'th digit of Omega is 1, otherwise it is all 0's.
Do you agree that every entry in the list is computable? Do you think that the diagonal is therefore computable?
> If you believe that you have a list of all computable Reals, I can > use a diagonal argument to explicitly construct a Real not on the > list. This number is obviously computable; Cantor provides an > explicit algorithm for constructing it, which can be implemented in > a few lines of code or in a TM.
Again, look up the definition of "computable number". Note carefully the absence of the Turing machine being provided with an infinite list of infinite sequences.
Come back when you have at least checked a basic definition of the terms you are using.