Date: Nov 22, 2012 3:54 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!
On 22 Nov., 20:22, William Hughes <wpihug...@gmail.com> wrote:

> Note that I was able to handle your

> "simple" case using induction.

>

> I consider the following case easy.

> If you disagree maybe you can say

> why?

>

> Consider the sequence of real numbers

>

> 1.0

> 10.0

> 100.0

> ...

>

> The limit is oo (unbounded)

>

> According to set theory, the number of 1's in the limit

> is 0. (The limit of the set of positions at which we

> have a 1 is the empty set).

Why should the 1 disappear completely? But let's assume it.

According to analysis the number of 1's in the limit is 1 and the

number of zeros left to the point is infinite. Proof by failure: Try

to establish in analysis the limit oo without 1 by the sequence

0

00

000

...

>

> Your contention: This is a contradiction. You cannot get oo

> with only 0's

My contention is same as before: Obviously set theory cannot reproduce

the results of analysis.

>

> My contention: The two limits are different and there is

> no contradiction.

You try to justify one error by another one. Set theory cannot

reproduce mathematics. That fact is not mended by constructing another

failure. But you see it better here

> > 01.

> > 0.1

> > 010.1

> > 01.01

> > 0101.01

> > 010.101

> > 01010.101

> > 0101.0101

> > ...

where set theory yields no digit and analysis yields inifinitely many

digits left to the point.

Taking the result of set theory seriously, we get a limit less than 1.

And in your example we can get rid of a 1 and have a limit oo with

only zeros. Do you think to defend set theory by that arguing? Should

really somebody take it seriously? And apply it anywhere? I don't

believe so.

Regards, WM