```Date: Mar 13, 2013 1:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 13 Mrz., 17:59, William Hughes <wpihug...@gmail.com> wrote:> On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:>> <snip>>> > > If you wish to contest this, use my words not> > > yours  (e.g.  I have never said "The list contains more> > > numbers than fit into a single line",  I have said> > > "There is no line in the list which contains every> > > number in the list".)>> > Correct. The list has more numbers than a single line has. Since every> > number that is in the list, must be in at least one line, this implies> > that the numbers are in more than one line.>> To be precise, a set of lines, say K, that contains all the numbers> contains at least two lines.In actual infinity, this is not avoidable.We note: At least two lines belong to the set that contains allnumbers. We call these lines necessary lines.So the set of necessary lines is not empty.>  However, this does *not* imply that> there are two numbers that are not in a single line.Why then should two lines be necessary?One being the substitute in case the other falls ill?> Nor does it imply that there is a necessary line in K.If there is not one necessary line, then there are two or morerequired.Proof: If you remove all lines from the list, then there remains noline and no number.> Note that a sufficient set does not imply a necessary line> even in potential infinity.  There is no line that is needed> to make L have an unfindable last line.So you believe that there can remain all numbers in the list afterremoving all lines? That is a remarkable claim. I would not accept itin mathematics.Note in actual infinity it makes sense to talk about all lines and toremove all lines.Regards, WM
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