On 7 Feb., 10:50, William Hughes <wpihug...@gmail.com> wrote:
For esay reference:
1) For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n). 2) For every n: (a_n1, a_n2, ..., a_nn) is terminating. 3) For every n: (d_1, d_2, ..., d_n) is terminating.
4) For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n). 5) For all n: (a_n1, a_n2, ..., a_nn) is terminating. 6) For all n: (d_1, d_2, ..., d_n) is terminating.
> WM uses induction to show that for every natural > number n, d is not the nth line of the list. > He then uses the fact that this is equivalent to > "there does not exist an m, such that d is the mth > line of the list". At no time does he assume that > "all" lines exist.-
I assume that all lines exist. I do not agree that 4 follows from 1 and 5 follows from 2 while ~6 follows from 3.
