```Date: Feb 14, 2013 2:26 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 13 Feb., 23:22, William Hughes <wpihug...@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 yAnd just this criterion is satisfied for the system112123...For every n all FISs of d are identical with all FISs of line n.> No concept of completeness is needed or used.That means we have to go to n only.>> 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,...}And the three points stand for every finite number, but not for all.>> Consider the list of potentially infinite sequence> L1=> 1000...> 11000...> 111000...> ...>> L2=> 111...> 11000...> 111000...> ...>> The diagonals are both> d=111...And again you confuse every with all.>> It makes perfect sense to say that there> is no line in L1 that is equal> to dPerfect sense?Do you claim that the list112123...does not contain every FIS of d?Do you claim that there are two or more FISs of d that require morethan one line for their accomodation?We can use induction to show that!Ponder about this question and then try to make perfect sense.Regards, WM
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