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 "t
Hi Mirek,
Le 19-nov.-07, à 20:14, Mirek Dobsicek a écrit :
>
> Hi Bruno,
>
> thank you for posting the solutions. Of course, I solved it by myself
> and it was a fine relaxing time to do the paper work trying to be
> rigorous, however, your solutions gave me additional insights, nice.
>
> I am
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.
>>
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 -
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
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
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 complemen
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 questi
You're saying that, just because you can *write down* the missing
sequence (at the beginning, middle or anywhere else in the list), it
follows that there *is* no missing sequence. Looks pretty wrong to me.
Cantor's proof disqualifies any candidate enumeration. You respond
by saying, "we
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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