In article <email@example.com>, firstname.lastname@example.org wrote:
> On Thursday, 19 December 2013 17:16:29 UTC+1, wpih...@gmail.com wrote: > > > However, note that when we use a indirect proof we use one and only one > > > > rational approximation to d. > > > Your proof holds for every fraction represented by every sum of d_n/10^n. > Note however, the "infinite sum" is not a sum (that is only a sloppy kind of > speech) but it is the limit of a sequence (of partial sums). Every partial > sum has a decimal expansion. The limit has not (because all finite natural > numbers n have been used up already and other natural numbers are not > available).
The point is that every rational has a decimal expanson accurate to any finite number of decimal places.
So in any list of rationals , the nth rational can be correctly known at its nth decimal place and d may be made to differ from it at that place.
Thus the construction which proves WM wrong is right! --