On 16 Jun., 14:05, "J. Clarke" <jclarke.use...@cox.net> wrote: > On 6/15/2010 11:59 AM, Aatu Koskensilta wrote: > > > > > > > WM<mueck...@rz.fh-augsburg.de> 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?
All definable real numbers and all their possible representations are contained in that list. This list is a list of everything. The alphabets and the languages and the dictionaries are given in later lines. It is very probable that every line has many different meaning, but no line has uncounatbly many meanings. Therefore the list contains only countably many finite definitions. And obviously the list cannot be diagonalized - like every meaningful list of meaningfuls words.