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 d


And in neither is there a line 000..., the anti-d.
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