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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