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. --
