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
Russell:
Maybe you might be interested in gfortran(http://gcc.gnu.org/wiki/
GFortran)?
Ronald
On Jun 2, 6:38 pm, russell standish li...@hpcoders.com.au wrote:
On Tue, Jun 02, 2009 at 07:45:22AM -0700, ronaldheld wrote:
Bruno:
Since I program in
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
Hi Jesse,
On 01 May 2009, at 19:36, Jesse Mazer wrote:
I found a paper on the Mandelbrot set and computability, I
understand very little but maybe Bruno would be able to follow it:
http://arxiv.org/abs/cs.CC/0604003
The same author has a shorter outline or slides for a presentation
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 03 Jun 2009, at 20:11, Jason Resch wrote:
On Fri, May 22, 2009 at 4:37 PM, Bruno Marchal marc...@ulb.ac.be
wrote:
Do you believe if we create a computer in this physical
universe that it could be made conscious,
But a computer is never conscious, nor is a brain. Only a person is
Hi Ronald,
On 02 Jun 2009, at 16:45, ronaldheld wrote:
Bruno:
Since I program in Fortran, I am uncertain how to interpret things.
I was alluding to old, and less old, disputes again programmers, about
which programming language to prefer.
It is a version of Church Thesis that all
From my understanding of logic, there is made the distinction between
objects and descriptions of objects.
For example, the relation is less than is considered different from
the relation symbol
So what you said makes sense.
Bruno Marchal wrote:
Hi Ronald,
On 02 Jun 2009, at 16:45,
On Thu, Jun 4, 2009 at 9:29 AM, Bruno Marchal marc...@ulb.ac.be wrote:
On 03 Jun 2009, at 20:11, Jason Resch wrote:
On Fri, May 22, 2009 at 4:37 PM, Bruno Marchal marc...@ulb.ac.be
wrote:
Do you believe if we create a computer in this physical
universe that it could be made conscious,
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
Bruno Marchal wrote:
Hi Ronald,
On 02 Jun 2009, at 16:45, ronaldheld wrote:
Bruno:
Since I program in Fortran, I am uncertain how to interpret things.
I was alluding to old, and less old, disputes again programmers, about
which programming language to prefer.
It is a
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.
On 04 Jun 2009, at 19:28, Brent Meeker wrote:
Bruno Marchal wrote:
Hi Ronald,
On 02 Jun 2009, at 16:45, ronaldheld wrote:
Bruno:
Since I program in Fortran, I am uncertain how to interpret things.
I was alluding to old, and less old, disputes again programmers,
about
which
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 or
Bruno Marchal wrote:
...
Bruno Marchal wrote:
The whole point of logic is to consider the Peano's axioms as a
mathematical object itself, which is studied mathematically in the
usual informal (yet rigorous and typically mathematica) way.
PA, and PA+GOLDBACH are different mathematical
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
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