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
On 20/11/2007, Bruno Marchal [EMAIL PROTECTED] wrote:
David, are you still there? This is a key post, with respect to the
Church Thesis thread.
Sorry Bruno, do forgive me - we seem destined to be out of synch at
the moment. I'm afraid I'm too distracted this week to respond
adequately - back
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
Hi,
David, are you still there? This is a key post, with respect to the
Church Thesis thread.
So let us see that indeed there is no bijection between N and 2^N =
2X2X2X2X2X2X... = {0,1}X{0,1}X{0,1}X{0,1}X... = the set of infinite
binary sequences.
Suppose that there is a bijection between N
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
Bruno Marchal skrev:
But then the complementary sequence (with the 0 and 1
permuted) is
also well defined, in Platonia or in the mind of God(s)
0 1 1 0
1 1 ...
But this infinite sequence cannot be in the list, above.
The "God" in question has to ackonwledge that.
The
Torgny Tholerus wrote:
Bruno Marchal skrev:
But then the complementary sequence (with the 0 and 1 permuted) is
also well defined, in Platonia or in the mind of God(s)
*0* *1* *1* *0* *1* *1* ...
But *this* infinite sequence cannot be in the list, above. The God
in question has to
meekerdb skrev:
Torgny Tholerus wrote:
An ultrafinitist comment to this:
==
You can add this complementary sequence to the end of the list. That
will make you have a list with this complementary sequence included.
But then you can make a new complementary sequence, that is
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