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