In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Matheology § 154: Consistency Proof! > > The long missed solution of an outstanding problem came from a > completely unexpected side: Social science proves the consistency of > matheology by carrying out a poll. > > As recently reported (see matheology § 152) > http://www.hs-augsburg.de/~mueckenh/KB/Matheology.pdf > mathematics and matheology lead to different values of the continued > fraction > > 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ = 0 (Cauchy) > 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ > 1 (Cantor)
It is not at all clear that these expressions represent any continued fraction at all.
Finite continued fractions look like a_0, or a_0 + 1/a_1, or a_0 + 1/(_ 1 + 1/a_2) or a_0 + 1/(a_1 + 1/(a_2 + 1/a_3)) or a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/a_4))) and so on
where a_0 is necessarily an integer and each of the other a_i's is a necessarily a POSITIVE integer, with the infinite case merely extending the finite cases endlessly.
But it is not at all clear what value any of the a_i would have to have in an expression like "1/((((((10^0)/10)+10^1)/10)+10^2)/10)+"