On 2010-06-18, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Give me a list of all computable Reals.
I specified such a list previously in this thread. It is not a computable list, but you didn't ask for a computable list - just a list of computable reals. They are not the same thing.
> I will use Cantor's diagonal argument to explicitly construct a Real > which isn't on the list. This is diagonal number clearly computable
In this case it clearly is not computable.
> as there is an explicit construction for it.
No, there is only a finite algorithm *relative to* being provided with the list initially. There is no algorithm to produce the antidiagonal starting without input, which being computable would require.
Come back when you read what the term "computable number" means.