Le 30-janv.-08, à 13:43, Mirek Dobsicek wrote (in different posts):
2\ Bruno, you recently wrote that you do not agree with Wolfram's
Principle of Computational Equivalence. As I understand to that
principle, Wolfram says that universe is a big cellular automata. What
is the evidence that
Date: Tue, 20 Nov 2007 19:01:38 +0100
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: Bijections (was OM = SIGMA1)
Bruno Marchal skrev:
But infinite ordinals can be different, and still have the same
cardinality. I have given
Le 20-nov.-07, à 17:59, meekerdb a écrit :
Bruno Marchal wrote:
.
But infinite ordinals can be different, and still have the same
cardinality. I have given examples: You can put an infinity of linear
well founded order on the set N = {0, 1, 2, 3, ...}.
What is the definition of linear
Le 19-nov.-07, à 17:00, Torgny Tholerus a écrit :
Torgny Tholerus skrev: If you define the set of all natural numbers
N, then you can pull out the biggest number m from that set. But this
number m has a different type than the ordinary numbers. (You see
that I have some sort of type
Bruno Marchal skrev:
To sum up; finite ordinal and finite cardinal coincide. Concerning
infinite number there are much ordinals than cardinals. In between
two different infinite cardinal, there will be an infinity of ordinal.
We have already seen that omega, omega+1, ... omega+omega,
Le 20-nov.-07, à 12:14, Torgny Tholerus a écrit :
Bruno Marchal skrev:
To sum up; finite ordinal and finite cardinal coincide. Concerning
infinite number there are much ordinals than cardinals. In between
two different infinite cardinal, there will be an infinity of ordinal.
We have
Bruno Marchal wrote:
.
But infinite ordinals can be different, and still have the same
cardinality. I have given examples: You can put an infinity of linear
well founded order on the set N = {0, 1, 2, 3, ...}.
What is the definition of linear well founded order? I'm familiar
with well
Bruno Marchal skrev:
But infinite ordinals can be different, and still have the same
cardinality. I have given examples: You can put an infinity of linear
well founded order on the set N = {0, 1, 2, 3, ...}.
The usual order give the ordinal omega = {0, 1, 2, 3, ...}. Now omega+1
is the
Quentin Anciaux skrev:
Hi,
Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit :
What do you mean by "each" in the sentence "for each natural number"? How
do you define ALL natural numbers?
There is a natural number 0.
Every
Le Friday 16 November 2007 09:33:38 Torgny Tholerus, vous avez écrit :
Quentin Anciaux skrev:
Hi,
Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit :
What do you mean by each in the sentence for each natural number?
How do you define ALL natural numbers?
There
Le 15-nov.-07, à 14:45, Torgny Tholerus a écrit :
Bruno Marchal skrev:Le 14-nov.-07, à 17:23, Torgny Tholerus a écrit :
What do you mean by ...?
Are you asking this as a student who does not understand the math, or
as a philospher who, like an ultrafinist, does not believe in the
Bruno Marchal wrote:
...
If not, let us just say that your ultrafinitist hypothesis is too
strong to make it coherent with the computationalist hypo. It means
that you have a theory which is just different from what I propose.
And then I will ask you to be ultra-patient, for I prefer to
Le 16-nov.-07, à 09:33, Torgny Tholerus a écrit :
There is a natural number 0.
Every natural number a has a natural number successor, denoted by
S(a).
What do you mean by Every here?
Can you give a *non-circular* definition of this word? Such that: By
every natural number I mean
Bruno Marchal skrev:
Le 15-nov.-07, 14:45, Torgny Tholerus a crit :
But m+1 is not a number.
This means that you believe there is a finite sequence of "s" of the
type
A =
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(
Le 14-nov.-07, à 17:23, Torgny Tholerus a écrit :
Bruno Marchal skrev:
0) Bijections
Definition: A and B have same cardinality (size, number of elements)
when there is a bijection from A to B.
Now, at first sight, we could think that all *infinite* sets have the
same cardinality,
Bruno Marchal skrev:
Le 14-nov.-07, 17:23, Torgny Tholerus a crit :
What do you mean by "..."?
Are you asking this as a student who does not understand the math, or
as a philospher who, like an ultrafinist, does not believe in the
potential infinite (accepted by
Hi,
Le Thursday 15 November 2007 14:45:24 Torgny Tholerus, vous avez écrit :
Bruno Marchal skrev:
Le 14-nov.-07, à 17:23, Torgny Tholerus a écrit :
What do you mean by each x here?
I mean for each natural number.
What do you mean by each in the sentence for each natural number? How
Bruno Marchal skrev:
0) Bijections
Definition: A and B have same cardinality (size, number of elements)
when there is a bijection from A to B.
Now, at first sight, we could think that all *infinite* sets have the
same cardinality, indeed the cardinality of the infinite set N. By N,
I
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