```Date: Feb 13, 2013 5:26 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <c50550cd-6bce-425c-a985-b9e419605161@o5g2000vbp.googlegroups.com>, William Hughes <wpihughes@gmail.com> wrote:> On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> <snip>> > > You cannot discern that two potentially infinity sequences are equal.> > When will you understand that such a result requires completeness?> > Nope> > Two potentially infinite sequences x and y are> equal iff for every natural number n, the> nth FIS of x is equal to the nth FIS of y> No concept of completeness is needed or used.> > E.G,> > we can use induction to show> > x={1,1+2,1+2+3,...,1+2+...+n,...}> > is equal to> > y={(1)(2)/2,(2)(3)/2,(3)(4)/2,...,n(n+1)/2,...}> > > Consider the list of potentially infinite sequence> L1=> 1000...> 11000...> 111000...> ...> > L2=> 111...> 11000...> 111000...> ...> > The diagonals are both> d=111...> > It makes perfect sense to say that there> is no line in L1 that is equal> to d but there is a line in L2 that is equal> to dAnd in neither is there a line 000..., the anti-d.--
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