```Date: Feb 25, 2013 9:08 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <5576043b-977f-4bd0-a2ac-3717ca1b4a20@d11g2000yqe.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 25 Feb., 13:46, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 25, 1:09 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > On 25 Feb., 12:20, William Hughes <wpihug...@gmail.com> wrote:> > > > Only those people who care> > > > about unfindable natural numbers (a group that> > > > includes WM but not me) are interested> >> > > No? The numbers of those lines that contain what, according to your> > > assertion, cannot be contained in one line, are unknowable> >> > [The term is "unfindable"]> > Wrong. You can easily define what line is requires, bamely the first> line of your asserted set of infinitely many lines that are necessary> to contain more than one line can contain.> > You cannot know that first line, because every line can be proven to> be *not* such a line.In a world more sane than WMytheology, if every line is not a last line, there is no last line.> > Your assertion can be proven wrong for *every* line. But you believe> that it is right for infinitely many? Mathematics looks different! What is wrong for individuals can be right for a set of those individuals.> >> > Nonsense.  The "numbers of those lines that contain what, according to> > your> > assertion, cannot be contained in one line" is a set of numbers,> > no single number has this property.> > I know that every number n has the property that the line l_n contains> all that its predecessors contain. Note, these n are numbers.Find us one that contains all that its successors do.> > > The set is the potentially> > infinite set {1,2,3,...}.  All of these are "findable".  I do not use> > and am not interested in "unfindable" natural numbers.> > Once upon a time you have been asserting that more than one line are> necessary to contain all that can be contained of d. If, as in your examples, each line, l, is a FIS of d, but not all of d, then no one line can contain what the next line contains, and every next line is necessary to get all of d.> This collection> of lines may be a set - it does not matter. But every set of lines of> L has a first element. You cannot name the first element l_n, you> cannot name the n. And that is a number.And that is all irrelevant to the fact that you cannot have it all when you insist on stopping before getting it all.WM's world does not allow induction as a method of proof, because it always requires stopping after a finite number of  steps.--
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