```Date: Feb 14, 2013 4:11 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 14 Feb., 22:02, Virgil <vir...@ligriv.com> wrote:> In article> <8eb0782b-60e7-4128-a03a-d1562cf4c...@g16g2000vbf.googlegroups.com>,>>>>>>  WM <mueck...@rz.fh-augsburg.de> wrote:> > 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 y> > > No concept of completeness is needed or used.>> > Remember, there are only finite initial segments.>> But infinitely many of them!Do you miss one of them in all lines of the list? Or is each one ininfinitely many lines? So you can choose one of these infinitely manylines in order to get FIS(n) of d.>> > The list contains every finite initial segment of d.> > Do you agree?>> IrrelevantIn fact, it is irrelevant whether you agree.>> > Every finite initial segment is finite.> > Do you agree?>> IrrelevantPlease note, I did not ask you.>>> > What do you conclude?>> That for every finite line d is longer than that lineYou think that d in actually infinite. It is not. It stretches fromd_1 to the d_n of your choice. And exactly the same is in infinitelymany lines. Of course you can choose whatever n you like (because thatis the meaning of potentially infinite: you can choose whatever n youlike).Regards, WM
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