2009/6/17 Torgny Tholerus tor...@dsv.su.se:
Bruno Marchal skrev:
Torgny,
I agree with Quentin.
You are just showing that the naive notion of set is inconsistent.
Cantor already knew that, and this is exactly what forced people to
develop axiomatic theories. So depending on which theory of
Bruno Marchal skrev:
Torgny,
I agree with Quentin.
You are just showing that the naive notion of set is inconsistent.
Cantor already knew that, and this is exactly what forced people to
develop axiomatic theories. So depending on which theory of set you
will use, you can or cannot
Torgny,
I agree with Quentin.
You are just showing that the naive notion of set is inconsistent.
Cantor already knew that, and this is exactly what forced people to
develop axiomatic theories. So depending on which theory of set you
will use, you can or cannot have an universal set (a set
On 12 Jun 2009, at 17:16, A. Wolf wrote:
We agree then.
Yes, it's my fault for creating a semantics argument. I'm usually
too busy
to even read the list...every once in a while something pops up and
I feel
obliged to comment even when it's the middle of a conversation.
No
On 12 Jun 2009, at 20:31, Jesse Mazer wrote:
Even for just an arithmetical realist. (All mathematicians are
arithmetical realist, much less are mathematical realist. I am not
an arithmetical realist).
I assume you meant to write I am not a mathematical realist?
Yes.
OK, but this
2009/6/14 Torgny Tholerus tor...@dsv.su.se:
Quentin Anciaux skrev:
Well it is illegal regarding the rules meaning with these rules set B
does not exist as defined.
What is it that makes set A to exist, and set B not to exist? What is
the (important) differences between the definition of
2009/6/13 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Fri, 12 Jun 2009 18:40:14 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
It is, as I said above, for me and all other humans to understand
Quentin Anciaux skrev:
2009/6/13 Torgny Tholerus tor...@dsv.su.se:
What do you think about the following deduction? Is it legal or illegal?
---
Define the set A of all sets as:
For all x holds that x belongs to A if and only if x is a set.
This is an general rule
Well it is illegal regarding the rules meaning with these rules set B
does not exist as defined.
2009/6/13 Torgny Tholerus tor...@dsv.su.se:
Quentin Anciaux skrev:
2009/6/13 Torgny Tholerus tor...@dsv.su.se:
What do you think about the following deduction? Is it legal or illegal?
Date: Sat, 13 Jun 2009 11:05:22 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Fri, 12 Jun 2009 18:40:14 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
There, they call arithmetic soundness what me (and many logician) call
soundness, when they refer to theories about numbers. Like Mendelson I
prefer to use the term logically valid, to what you call soundness.
I may have misstated myself, but the wiki article you pointed me to agrees
with
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Countably infinite does not mean recursively countably infinite.
This is something which I will explain in the seventh step thread.
There is theorem by Kleene which links Post-Turing degrees of
unsolvability with the shape of arithmetical
Le 12-juin-09, à 09:31, Bruno Marchal a écrit :
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Ah, that makes sense--I hadn't thought of combining multiple
universal quantifiers in that way, but obviously you can do so and
get a meaningful statement about arithmetic that for a
Le 12-juin-09, à 08:28, A. Wolf a écrit :
There, they call arithmetic soundness what me (and many logician)
call
soundness, when they refer to theories about numbers. Like
Mendelson I
prefer to use the term logically valid, to what you call soundness.
I may have misstated myself,
Logicians from different fields use terms in different ways. In
provability logic and in recursion theory, soundness means often
arithmetical soundness.
I understand.
Part of the reason for my particular viewpoint: there's a group of
professors at the college I work at who are working on
Jesse Mazer skrev:
Date: Wed, 10 Jun 2009 09:18:10 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Tue, 9 Jun 2009 18:38:23 +0200
From: tor...@dsv.su.se
To: everything-list
Date: Fri, 12 Jun 2009 18:40:14 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Wed, 10 Jun 2009 09:18:10 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Date: Fri, 12 Jun 2009 09:31:46 +0200
On 11 Jun 2009, at 21:43, Jesse Mazer wrote:
Countably infinite does not mean recursively countably infinite. This is
something which I
On 10 Jun 2009, at 20:00, Brent Meeker wrote:
Bruno Marchal wrote:
On 10 Jun 2009, at 02:20, Brent Meeker wrote:
I think Godel's imcompleteness theorem already implies that there
must
be non-unique extensions, (e.g. maybe you can add an axiom either
that
there are infinitely many
On 10 Jun 2009, at 20:17, Jesse Mazer wrote:
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Date: Wed, 10 Jun 2009 18:03:26 +0200
On 10 Jun 2009, at 01:50, Jesse Mazer wrote:
Such an hypercomputer is just what Turing
As I said, you can formalize the notion of soundness in Set Theory. But
this adds nothing, except that it shows that the notion of soundness has
the same level of complexity that usual analytical or topological set
theoretical notions. So you can also say that unsound means violation
On 11 Jun 2009, at 14:48, A. Wolf wrote:
As I said, you can formalize the notion of soundness in Set
Theory. But
this adds nothing, except that it shows that the notion of
soundness has
the same level of complexity that usual analytical or topological
set
theoretical notions.
A. Wolf wrote:
As I said, you can formalize the notion of soundness in Set Theory. But
this adds nothing, except that it shows that the notion of soundness has
the same level of complexity that usual analytical or topological set
theoretical notions. So you can also say that unsound
Jesse Mazer skrev:
Date: Tue, 9 Jun 2009 18:38:23 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
For you to be able to use the word all, you must define the domain
of that word. If you do not define
-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical argument is about the mening of the word all. To be
able to use that word, you must associate it with a value set.
What's a value set? And why do you say we must associate it in
this way
On 10 Jun 2009, at 01:50, Jesse Mazer wrote:
Isn't this based on the idea that there should be an objective truth
about every well-formed proposition about the natural numbers even
if the Peano axioms cannot decide the truth about all propositions?
I think that the statements that
On 10 Jun 2009, at 02:20, Brent Meeker wrote:
I think Godel's imcompleteness theorem already implies that there must
be non-unique extensions, (e.g. maybe you can add an axiom either that
there are infinitely many pairs of primes differing by two or the
negative of that). That would seem
On 10 Jun 2009, at 04:14, Jesse Mazer wrote:
I think I remember reading in one of Roger Penrose's books that
there is a difference between an ordinary consistency condition
(which just means that no two propositions explicitly contradict
each other) and omega-consistency--see
Bruno Marchal wrote:
On 10 Jun 2009, at 02:20, Brent Meeker wrote:
I think Godel's imcompleteness theorem already implies that there must
be non-unique extensions, (e.g. maybe you can add an axiom either that
there are infinitely many pairs of primes differing by two or the
negative
Date: Wed, 10 Jun 2009 09:18:10 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Tue, 9 Jun 2009 18:38:23 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Date: Wed, 10 Jun 2009 18:03:26 +0200
On 10 Jun 2009, at 01:50, Jesse Mazer wrote:
Isn't this based on the idea that there should be an objective truth about
every well-formed
Of course, Torgny stops, in the UD Argument, at step 0. He disbelieves
classical computationalism.
The yes doctor is made senseless; because he is a zombie, and
Church thesis becomes senseless, because he is ultrafinitist, and
Church thesis concerns functions from N to N, or from N to 2,
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical argument is about the mening of the word all. To be
able to use that word, you must associate
2009/6/9 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical argument is about the mening of the word all
Quentin Anciaux wrote:
2009/6/9 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical argument is about
Meeker meeke...@dslextreme.com:
Quentin Anciaux wrote:
2009/6/9 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical
: Re: The seven step-Mathematical preliminaries
My philosophical argument is about the mening of the word all. To be
able to use that word, you must associate it with a value set.
What's a value set? And why do you say we must associate it in
this way? Do you have a philosophical
Meeker meeke...@dslextreme.com:
Quentin Anciaux wrote:
2009/6/9 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
My philosophical
Quentin Anciaux wrote:
You have to explain why the exception is needed in the first place...
The rule is true until the rule is not true anymore, ok but you have
to explain for what sufficiently large N the successor function would
yield next 0 and why or to add that N and that exception to
Date: Tue, 9 Jun 2009 18:38:23 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re
2009/6/9 Brent Meeker meeke...@dslextreme.com:
Quentin Anciaux wrote:
You have to explain why the exception is needed in the first place...
The rule is true until the rule is not true anymore, ok but you have
to explain for what sufficiently large N the successor function would
yield next
2009/6/9 Quentin Anciaux allco...@gmail.com:
2009/6/9 Brent Meeker meeke...@dslextreme.com:
Quentin Anciaux wrote:
You have to explain why the exception is needed in the first place...
The rule is true until the rule is not true anymore, ok but you have
to explain for what sufficiently
A good model of the naturalist math that Torgny is talking about is the
overflow mechanism in computers.
For example in a 64 bit machine you may define overflow for positive
integers as 2^^64 -1. If negative integers are included then the
biggest positive could be 2^^32-1.
Torgny would also
Date: Tue, 9 Jun 2009 12:54:16 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
You don't justify definitions. How would you justify Peano's axioms as being
the right ones? You are just confirming my
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 12:54:16 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
You don't justify definitions. How would you justify Peano's axioms
as being
the right ones? You
2009/6/10 Brent Meeker meeke...@dslextreme.com:
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 12:54:16 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
You don't justify definitions. How would you justify
Date: Tue, 9 Jun 2009 15:22:10 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 12:54:16 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 15:22:10 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 12:54:16 -0700
From: meeke...@dslextreme.com
Date: Tue, 9 Jun 2009 17:20:39 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer wrote:
Date: Tue, 9 Jun 2009 15:22:10 -0700
From: meeke...@dslextreme.com
To: everything-list@googlegroups.com
On Sat, Jun 06, 2009 at 10:22:11AM -0700, Brent Meeker wrote:
I wonder if anyone has tried work with a theory of finite numbers: where
BIGGEST+1=BIGGEST or BIGGEST+1=-BIGGEST as in some computers?
Brent
The numbers {0,...,p-1} with p prime, and addition and multiplication
given modulo p
Marty,
On 07 Jun 2009, at 02:03, Brent Meeker wrote:
m.a. wrote:
*Okay, so is it true to say that things written in EXTENSION are
never
in formula style but are translated into formulas when we put them
into INTENSION form? You can see that my difficulty with math
arises from an
: Re: The seven step-Mathematical preliminaries 2
m.a. wrote:
*Okay, so is it true to say that things written in EXTENSION are never
in formula style but are translated into formulas when we put them
into INTENSION form? You can see that my difficulty with math
arises from an inability
Bruno,
Yes, this seems very clear and will be helpful to refer back to if
necessary. m.a.
- Original Message -
From: Bruno Marchal marc...@ulb.ac.be
To: everything-list@googlegroups.com
Sent: Sunday, June 07, 2009 4:33 AM
Subject: Re: The seven step-Mathematical
On Sat, Jun 6, 2009 at 4:20 PM, Jesse Mazer laserma...@hotmail.com wrote:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
[[[
Date: Sat, 6 Jun 2009
: Bruno Marchal
To: everything-list@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
? ? A =
? ? B =
A ? ? =
B ? ? =
N ? ? =
B ? ? =
? ? B
: The seven step-Mathematical preliminaries 2
∅ ∪ A =
∅ ∪ B =
A ∪ ∅ =
B ∪ ∅ =
N ∩ ∅ =
B ∩ ∅ =
∅ ∩ B =
∅ ∩ ∅ =
∅ ∪ ∅ =
http://iridia.ulb.ac.be/~marchal/
--~--~-~--~~~---~--~~
You received
Marty, Kim,
I realize that, now, the message I have just sent does not have the
right symbols. Apparently my computer does not understand the
Thunderbird!
From now on I will use capital words for the mathematical symbols.
And I will write mathematical expression in bold.
For examples:
Jesse Mazer skrev:
Date: Fri, 5 Jun 2009 08:33:47 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Brian Tenneson skrev:
How can BIGGEST+1 be a natural number but not belong to the set of all
natural
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Fri, 5 Jun 2009 08:33:47 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re
Torgny Tholerus wrote:
Jesse Mazer skrev:
Date: Fri, 5 Jun 2009 08:33:47 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Brian Tenneson skrev:
How can BIGGEST+1 be a natural number but not belong
I wonder if anyone has tried work with a theory of finite numbers: where
BIGGEST+1=BIGGEST or BIGGEST+1=-BIGGEST as in some computers?
There is a group of faculty who address this problem directly in my
department. But any general-purpose computer can emulate true, unlimited
natural numbers
To: everything-list@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
∅ ∪ A =
∅ ∪ B =
A ∪ ∅ =
B ∪ ∅ =
N ∩ ∅ =
B ∩ ∅ =
∅ ∩ B =
∅ ∩ ∅ =
∅ ∪ ∅ =
---
To unsubscribe from this group, send email
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Here you're just contradicting yourself. If you say BIGGEST+1 is then
a natural number
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re
, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
∅ ∪ A =
∅ ∪ B =
A ∪ ∅ =
B ∪ ∅ =
N ∩ ∅ =
B ∩ ∅ =
∅ ∩ B =
∅ ∩ ∅ =
∅ ∪ ∅ =
---
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com
For more options, visit
Jesse Mazer wrote:
Date: Sat, 6 Jun 2009 21:17:03 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list
If it helps, here's a screenshot of how the symbols are supposed to look:
http://img34.imageshack.us/img34/3345/picture2uzk.png
From: marc...@ulb.ac.be
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries 2
Date: Sat, 6 Jun 2009 22:36:01 +0200
Marty,
Bruno
Marchal
To: everything-list@googlegroups.com
Sent: Saturday, June 06, 2009 4:36 PM
Subject: Re: The seven step-Mathematical preliminaries 2
We do have problem of symbols, with the mail. I don't see any rectangle in
the message below!
Take it easy and . We will go very slowly
To: everything-list@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
=== Intension and extension
In the case of finite and little set we have seen that we can define them
2009/6/6 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Here you're just contradicting yourself
-
From: Bruno Marchal
To: everything-list@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
∅ ∪ A =
∅ ∪ B =
A ∪ ∅ =
B ∪ ∅ =
N ∩ ∅ =
B ∩ ∅ =
∅ ∩ B =
∅ ∩ ∅ =
∅ ∪ ∅ =
---
To unsubscribe from
expression just slip out from my
mind. smaller than is much better! Thanks for helping,
Bruno
- Original Message -
From: Bruno Marchal
To: everything-list@googlegroups.com
Sent: Wednesday, June 03, 2009 1:15 PM
Subject: Re: The seven step-Mathematical preliminaries 2
On this date, you made the following correction: You cannot write D = 4*x
..., But you wrote D= 4*x in the exercise just above it. I don't get
the distinction between your use of the equation and mine.
- Original Message -
From: Bruno Marchal
Exercise 2: I will
m.a. wrote:
*Bruno,*
* I've encountered some difficulty with the examples below.
You say that in extension describes exhaustion or
quasi-exhaustion. And you give the example: **B = {3, 6, 9, 12, ...
99}.*
* Then you define in intension with exactly the same type
Bruno,
When I tried to copy the symbols from the URL cited below, I
found that my email server was not able to reproproduce the intersection or the
union symbol. See below:
From: Bruno Marchal
To: everything-list@googlegroups.com
∅ ∪ A = I see two
Quentin Anciaux wrote:
2009/6/6 Torgny Tholerus tor...@dsv.su.se:
Jesse Mazer skrev:
Date: Sat, 6 Jun 2009 16:48:21 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Jesse Mazer skrev:
Here
Okay, so is it true to say that things written in EXTENSION are never in
formula style but are translated into formulas when we put them into INTENSION
form? You can see that my difficulty with math arises from an inability to
master even the simplest definitions.marty a.
-
m.a. wrote:
*Okay, so is it true to say that things written in EXTENSION are never
in formula style but are translated into formulas when we put them
into INTENSION form? You can see that my difficulty with math
arises from an inability to master even the simplest definitions.
Brian Tenneson skrev:
On Thu, Jun 4, 2009 at 8:27 AM, Torgny Tholerus tor...@dsv.su.se
mailto:tor...@dsv.su.se wrote:
Brian Tenneson skrev:
Torgny Tholerus wrote:
It is impossible to create a set where the successor of every
element is
inside the
Kory Heath skrev:
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
2009/6/5 Torgny Tholerus tor...@dsv.su.se:
Kory Heath skrev:
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
Date: Fri, 5 Jun 2009 08:33:47 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Brian Tenneson skrev:
On Thu, Jun 4, 2009 at 8:27 AM, Torgny Tholerus tor...@dsv.su.se
mailto:tor...@dsv.su.se wrote
Torgny Tholerus wrote:
Brian Tenneson skrev:
On Thu, Jun 4, 2009 at 8:27 AM, Torgny Tholerus tor...@dsv.su.se
mailto:tor...@dsv.su.se wrote:
Brian Tenneson skrev:
Torgny Tholerus wrote:
It is impossible to create a set where the successor of every
From what you said earlier, BIGGEST={0,1,...,BIGGEST-1}. Then
BIGGEST+1={0,1,...,BIGGEST-1} union {BIGGEST} = {0,1,...,BIGGEST}.
Why would {0,1,...BIGGEST} not be a natural number while
{0,1,...,BIGGEST-1} is?
If {0, 1, ... , BIGGEST-1} is a natural number, then {0,1,...,BIGGEST} is
too,
10:03 AM
Subject: Re: The seven step-Mathematical preliminaries 2
Hi Marty,
On 05 Jun 2009, at 00:30, m.a. wrote:
Bruno,
I don't have dyslexia
Good news.
but my keyboard doesn't contain either the UNION symbol or the INTERSECTION
symbol
Brian Tenneson skrev:
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
If you are ultrafinitist then by definition the set N does not
exist... (nor any infinite set countably or not).
If you pose the assumption of a biggest number for N, you come to a
contradiction because you use the successor operation which cannot
admit a biggest number.(because N is well
On Thu Jun 4 1:15 , Bruno Marchal sent:
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
Quentin Anciaux skrev:
If you are ultrafinitist then by definition the set N does not
exist... (nor any infinite set countably or not).
All sets are finite. It it (logically) impossible to construct an
infinite set.
You can construct the set N of all natural numbers. But that set must
This is a denial of the axiom of infinity. I think a foundational set
theorist might agree that it is impossible to -construct- an infinite
set from scratch which is why they use the axiom of infinity.
People are free to deny axioms, of course, though the result will not be
like ZFC set
Brian Tenneson skrev:
This is a denial of the axiom of infinity. I think a foundational set
theorist might agree that it is impossible to -construct- an infinite
set from scratch which is why they use the axiom of infinity.
People are free to deny axioms, of course, though the result will
Torgny Tholerus wrote:
Brian Tenneson skrev:
This is a denial of the axiom of infinity. I think a foundational set
theorist might agree that it is impossible to -construct- an infinite
set from scratch which is why they use the axiom of infinity.
People are free to deny axioms, of
Hi Marty,
On 04 Jun 2009, at 01:11, m.a. wrote:
Bruno,
I stopped half-way through because I'm not at all sure of
my answers and would like to have them confirmed or corrected, if
necessary, rather than go on giving wrong answers. marty a.
No problem.
Exercise 1: Could
On Thu, Jun 4, 2009 at 7:28 AM, kimjo...@ozemail.com.au
kimjo...@ozemail.com.au wrote:
On Thu Jun 4 1:15 , Bruno Marchal sent:
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
I've never seen an ultrafinitist definition of the natural numbers.
The usual definition via Peano's axioms obviously rules out there being
a largest number. I would suppose that an ultrafinitist definition of
the natural numbers would be something like seen in a computer (which is
Torgny Tholerus wrote:
Brian Tenneson skrev:
This is a denial of the axiom of infinity. I think a foundational set
theorist might agree that it is impossible to -construct- an infinite
set from scratch which is why they use the axiom of infinity.
People are free to deny axioms, of
On 04 Jun 2009, at 15:40, Brian Tenneson wrote:
This is a denial of the axiom of infinity. I think a foundational
set theorist might agree that it is impossible to -construct- an
infinite set from scratch which is why they use the axiom of infinity.
People are free to deny axioms, of
Torngy,
How many numbers do you think exist between 0 and 1? Certainly not
only the ones we define, for then there would be a different quantity
of numbers between 1 and 2, or 2 and 3.
Jason
On Thu, Jun 4, 2009 at 10:27 AM, Torgny Tholerus tor...@dsv.su.se wrote:
Brian Tenneson skrev:
Hi Kim,
On 04 Jun 2009, at 14:28, kimjo...@ozemail.com.au wrote:
OK - I find this quite mind-blowing; probably because I now
understand it for the first
time in my life. So how did it get this rather ridiculous name of
square root? What's it
called in French?
Racine carrée.
Date: Thu, 4 Jun 2009 15:23:04 +0200
From: tor...@dsv.su.se
To: everything-list@googlegroups.com
Subject: Re: The seven step-Mathematical preliminaries
Quentin Anciaux skrev:
If you are ultrafinitist then by definition the set N does not
exist... (nor any infinite set countably
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