On 6/15/2010 11:59 AM, Aatu Koskensilta wrote: > WM<firstname.lastname@example.org> writes: > >> We should not use oracles in mathematics. > > Nonsense. Using orcales we can show for example that the P = NP problem > can't be solved using any technique that relativizes. This is a useful > result. > >> A real is computable or not. My list contains all computable numbers: >> >> 0 >> 1 >> 00 >> ... > > Your list doesn't appear to contain any real at all, just finite binary > sequences.
Did someone redefine the real numbers to exclude all numbers that consist only of the digits 0 and 1?