On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Explain to me how my requirements for the input list of all > computable Reals is different to Cantor's requirements for the input > list of all Reals, other than the requirement that every item on the > list is computable?
It is not. Your error comes later.
Cantor's proof includes a construction taking a list L and defining an antidiagonal real antidiag(L) from it. Your error is supposing that this construction is a finite algorithm fitting the definition of "computable real". It is not. By stretching the definition of "algorithm" somewhat, it can be supposed to be an algorithm accepting finite input n and infinite input L, and producing the n'th antidiagonal digit. This is a stretch since algorithms are normally not supposed to have infinite inputs.
However, there is no way that you can then prove the existence of a finite algorithm accepting only the *finite* input n and producing the n'th antidiagonal digit.
> (in more modern terminology) that there is no recursively enumerable > mapping
Once again, "recursively enumerable" is an introduction purely of your own invention. It is not present in Cantor's proof, it is not present in a modern recasting of Cantor's proof, it has no relevance at all to Cantor's proof. Cantor's proof applies to *every* mapping from N to R.
