```Date: Mar 21, 2013 7:32 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

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 theinfinite set of lines are unnecessary?Note: For every finite set of natural numbers, we can look at allelements, at least in principle. We do not need induction for fixedfinite sets. Induction is not *necessary* then, so to speak.I hope you see that your claim is nonsense, iff there is an infiniteset 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 oneis lurking like a dragon?>> Once we remove one line, we are left with> a new set of unnecessary lines.  We can> remove one of these lines.> From induction we get that> any finite set of lines can> be removed.More. From induction we get that every set is finite. The error ofmatheology is to assume that there is more than every finite set, butthis "more" obviously cannot be determined by induction (because it isnot part of mathematics). Therefore any desired property could beattributed to this "more". However, it is not good taste to attributeproperties like "unnatural" or "green" or so to this "more".Our result is:If all natural numbers can be reached by induction, then nothingremains that makes the set |N actually infinite, because |N is notmore than all natural numbers.And if not all natural numbers can be reached by induction, then theremust be a first one of the "more" - at least, if the more consists ofnatural numbers.You see, your position is untenable - at least in mathematics.Regards, WM
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