```Date: Feb 26, 2013 4:54 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 26, 6:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 26 Feb., 13:11, William Hughes <wpihug...@gmail.com> wrote:> On Feb 26, 12:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > We both agree>> >  There does not exist an m> >  such that the mth line> >  of L is coFIS with the diagonal> >  (here we interpret "There does> >  not exist" to mean "we cannot find").>> > So we agree any such m must be an> > unfindable natural number.>> It is a variable that can take any natural number.OK, so we have constant natural numbersand variable natural numbers.We agree that any such m cannot bea constant natural number but mustbe a variable natural number.Now, in standard terminology (where thereis no such thing as a variablenatural number) we havea natural number valued function of time(or of the number of FISs of d that "actuallyexist", an increasing function of time)m(t).  It is trivial to see that thereis an m(t) such that the "actually existing"line with index m(t), contains all"actually existing" FISs of d.However, calling m(t) "the index of the linethat contains every FIS of d"strains language beyond the breaking point.Similarly, it follows by definitionof "actually existing", thatthere is a time varying function max(t),such that at any time max(t) is the maximumof the "actually existing" natural numbers.However, calling the function max(t)the largest element of the potentiallyinfinite set |N, is silly.Now no one can stop you using whateverterminology you want.  However, do notexpect that you can use idiotic terminologywithout being considered an idiot.
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