
Re: Matheology § 222 Back to the roots
Posted:
Mar 11, 2013 9:26 AM


WM <mueckenh@rz.fhaugsburg.de> writes:
> On 11 Mrz., 12:51, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: >> WM <mueck...@rz.fhaugsburg.de> writes: >> > On 9 Mrz., 16:00, William Hughes <wpihug...@gmail.com> wrote: >> >> So this is WM's explanation. >> >> >> When he says >> >> >> No findable line of L is coFIS >> >> with d >> >> >> and >> >> >> g is coFIS with d >> >> >> he is not using the same d. >> >> >> d like L_m is changable. >> >> >> So let us use (d) to indicate the function. >> >> The function (d) is not changable, though >> >> its value may be. >> >> > What do you understand by the not changeable function (d)? >> >> Can you understand that there is a function which, given any natural >> number n, can return the first n digits of the decimal expansion of pi? > > Of course. There is even a much simpler case, namely the function that > given n return n digits of 1/9. But we have to distinguish between > this function, abbreviated by "0.111..." and its values > 0.1 > 0.11 > 0.111 > ... > > Note here no actual infinity is involved unless 0.111... is assumed to > be a decimal fraction with more than any finite number of 1's.
And can you understand that it is possible to give a potentially infinite list of potentially infinite lists of digits, by a function f of two naturals, such that for every n,m, f(n,m) is the mth digit of the mth list?
Still no actual infinity, and the function is a fixed set of instructions.
> > Regards, WM
 Alan Smaill

