Date: Feb 13, 2013 5:22 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

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