On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Of course there exists a mapping from N to computable numbers. But > Cantor's proof requires more than that; it requires the mapping to > be recursively enumerable such that we can also explicitly list > them.
It does not. If you believe otherwise, feel free to show where in Cantor's proof any requirement for recursive enumerability is stated or implicitly used.
The simple fact is that no such requirement exists. Cantor's diagonal proof applies to *every* mapping from N to R, recursively enumerable or not, showing that no such mapping is surjective.
Your introduction of recursive enumerability into Cantor's proof is entirely your own fabrication.