On Jun 4, 2009, at 8:27 AM, Torgny Tholerus wrote:
How do you handle the Russell paradox with the set of all sets that
does
not contain itself? Does that set contain itself or not?
My answer is that that set does not contain itself, because no set can
contain itself. So the set of all
On Wed Jun 3 0:39 , Bruno Marchal marc...@ulb.ac.be sent:
Hi Kim, Hi Marty and others,
So it is perhaps time to do some math.
It is
Obviously this is a not a course in math, but it is an explanation
from scratch of the seven step of the universal dovetailer argument.
It is a
On 02 Jun 2009, at 22:00, Brent Meeker wrote:
Bruno Marchal wrote:
...
A set is entirely defined by its elements. Put in another way, we
will
say that two sets are equal if they have the same elements.
Exercise 6. Let S be the set {0, 1, 45} and let M be the set
described
by {45,
should not worry if they don't understand them.
Bruno
James
- Original Message
From: Bruno Marchal marc...@ulb.ac.be
To: everything-list@googlegroups.com
Sent: Tuesday, June 2, 2009 12:29:47 PM
Subject: Re: The seven step-Mathematical preliminaries
The beauty of all
Excellent!
Kim, are you OK with Marty's answers?
Does someone have a (non philosophical) problem?
I will be busy right now (9h22 am). This afternoon I will send the
next seven exercises.
Bruno
On 02 Jun 2009, at 21:57, m.a. wrote:
Bruno,
I appreciate the simplicity of the
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it by the infinite quasi exhaustion by
{0, 1, 2, 3, ...}.
Let N be the biggest
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it by the infinite quasi exhaustion by
{0, 1, 2, 3,
Quentin Anciaux skrev:
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Quentin Anciaux skrev:
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you
Quentin Anciaux kirjoitti:
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
...
How do you know that there is no biggest number?
You just did.
You shown that by assuming there is one it entails a contradiction.
Have you examined all
the natural numbers?
No, that's what demonstration
Date: Wed, 3 Jun 2009 13:14:16 +0200
Subject: Re: The seven step-Mathematical preliminaries
From: allco...@gmail.com
To: everything-list@googlegroups.com
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal
I don't know if Bruno is about to answer this in messages I haven't
checked yet but one can visualize the square root of 2. If you draw a
square one meter by one meter, then the length of the diagonal is the
square root of 2 meters. It is approximately 1.4. What's relevant to
Bruno's
How do you know that there is no biggest number? Have you examined all
the natural numbers? How do you prove that there is no biggest number?
In my opinion those are excellent questions. I will attempt to answer
them. The intended audience of my answer is everyone, so please forgive
Quentin Anciaux wrote:
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it
2009/6/3 Brent Meeker meeke...@dslextreme.com:
Quentin Anciaux wrote:
2009/6/3 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you
Very good answer, Kim,
Just a few comments. and then the sequel.
Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,
3, ...}?
No idea what square-root(2) means. When I said I was innumerate I
wasn't kidding! I could of course look
it up or ask my mathematics teacher
Thank you very much. I realized I made some false statements as well.
It seems likely that reliance on (not P - Q and not Q) - P being a
tautology is the easiest proof of there being no largest natural number.
Brent Meeker wrote:
Brian Tenneson wrote:
How do you know that
@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
=== Intension and extension
Before defining intersection, union and the notion of subset, I would like
to come back on the ways we can define some
On Wed, Jun 03, 2009 at 10:11:41AM -0400, Jesse Mazer wrote:
The English term for this is proof by contradiction:
http://en.wikipedia.org/wiki/Proof_by_contradiction
Funnily enough, we were taught to call this by the latin phrase
reductio ad absurdum. I think my maths prof came from
Thank you for starting this discussion. I have only joined recently and
have little knowledge of your research. To see it laid out in the
sequence you describe should make it clear to me what it is all about.
I'm particularly interested in the interaction between consciousness and
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it by the infinite quasi exhaustion by
{0, 1, 2, 3, ...}.
Let N be the biggest number in the set {0, 1, 2, 3, ...}.
Exercise: does the number N+1 belongs to the
Date: Tue, 2 Jun 2009 19:43:59 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe
On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
Thank you for starting this discussion. I have only joined recently
and
have little knowledge of your research. To see it laid out in the
sequence you describe should make it clear to me what it is all about.
I'm particularly interested
On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:
Bruno Marchal skrev:
4) The set of all natural numbers. This set is hard to define, yet I
hope you agree we can describe it by the infinite quasi exhaustion by
{0, 1, 2, 3, ...}.
Let N be the biggest number in the set {0, 1, 2, 3, ...}.
Thanks for the links. I'll look over them and hopefully I'll understand
what I see. At least if I have questions I can ask though maybe not in
this thread.
I don't yet know precisely what you mean by a machine but I do have
superficial knowledge of Turing machines; I'm assuming there is a
The beauty of all this, Brian, is that the correct (arithmetically)
universal machine will never been able to answer the question are you
a machine?, but she (it) will be able to bet she is a (unknown)
machine. She will never know which one, and she will refute all
theories saying which
PM
Subject: Re: The seven step-Mathematical preliminaries
The beauty of all this, Brian, is that the correct (arithmetically)
universal machine will never been able to answer the question are you
a machine?, but she (it) will be able to bet she is a (unknown)
machine. She will never know
Bruno,
I appreciate the simplicity of the examples. My answers follow the
questions.marty a.
- Original Message -
From: Bruno Marchal marc...@ulb.ac.be
= begin
===
1) SET
Informal
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