```Date: Mar 21, 2013 9:02 AM
Author: William Hughes
Subject: Re: Matheology § 224

On Mar 21, 12:32 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 21 Mrz., 11:36, William Hughes <wpihug...@gmail.com> wrote:>> > On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:>> > <snip>>> > > > There is such a thing as a sufficient set of> > > > lines  (all sufficient sets are composed> > > > entirely of unnecessary lines, which means> > > > that you can remove any finite set of lines>> > > Why only finite sets?>> > You can only use induction to prove> > stuff about finite sets.>> In fact? That's amazing. So we cannot prove that all lines of the> infinite set of lines are unnecessary?>We can prove that something is true for everymember of an infinite set.  We cannotprove that something is true for the setitself unless the set is finite.> Note: For every finite set of natural numbers, we can look at all> elements, at least in principle. We do not need induction for fixed> finite sets. Induction is not *necessary* then, so to speak.If you want to say that something is true for someparticular finite set you do not need inductionIf you want to say that something is true for eachfinite set, then you do need induction.If you want to say that something is true for eachinfinite set then induction will not help.>> I hope you see that your claim is nonsense, iff there is an infinite> set of natural numbers.>>>> > > What property is changed if infinitely many are> > > there? If there are infinitely many unnecessary lines, they all can be> > > removed - by their property of being unnecessary.>> > Nope, their property of being unnecessary means> > that *any one* line can be removed.>> But you think that after all finite and unnecessary lines another one> is lurking like a dragon?Now I think that after any finite set of unnecessary lines hasbeen removed, there still remains an unnecessary line.
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