On Sun, 13 Apr 2014 05:54:19 -0700, mueckenh wrote:
> On Sunday, 13 April 2014 14:07:54 UTC+2, Tommy Jensen wrote: > >> Let a(i) be the real number defined by the interpretation of the >> i'th >> sentence (in lexicographic ordering) of a language in which it defines >> a real number of D. For each i and j let b(i,j) be the binary bit of >> a(i) which is read j positions after the binarypoint. The let u be the >> real number between 0 and 1, excluding 1, for which its binary bit in >> the position j after the binarypoint is equal to 1-b(j,j). > > > First, do you believe that this very short sequence of letters is not in > the infinite list of finite expressions that I defined? You remember? > > 0 > 1 > ... > > Second, the list of finite definitions does not contain b(j,j). The > second bit of the second line is undefined. > Regards, WM
And with that, you not only have admitted to believing in a "set of definable real numbers" (and we note that "definable real number" is itself an undefined term), but you also now say that you believe in such real numbers that have undefined bits in their binary expansion. Or likely you misunderstood when I referred to the j'th bit of a real number. I meant the j'th bit of its binary expansion, counting j binary digits to the right of the binarypoint. Not the j'th bit of its finite definition, whatever that means. But you seem to believe in many things that neither you nor anyone else has ever encountered, so who knows.