Re: November 25 is Infinite Clause day!!
From: John Savard (jsavard_at_excxn.aNOSPAMb.cdn.invalid)
Date: 11/21/04
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Date: Sun, 21 Nov 2004 20:19:05 GMT
On Sun, 21 Nov 2004 18:00:06 GMT, The Ghost In The Machine
<ewill@sirius.athghost7038suus.net> wrote, in part:
>In sci.logic, David Bernier
><david250@videotron.ca>
> wrote
>on Sat, 20 Nov 2004 23:23:55 -0500
><vLUnd.98560$De5.1797114@wagner.videotron.net>:
>> HERC777 wrote:
>>> Merry X-count-mas!
>>>
>>> Do you believe in Infinite Clause? Will he make it to your real place
>>> in time and all of the infinite places and make something new for you?
>>>
>>> Have you been good and read your maths text so you too can see
>>> Infinite Clause? He's keeping a list and he's checking it twice!
>>>
>>> CANTOR :
>>> The uncountable number does not have the 1st digit of the 1st
>>> countable number.
>>>
>>> UTM(neN,d) :
>>> ALL 10 digits are present in the 1st digit place an infinite number of
>>> times, on the list of computable reals.
>>>
>>> CANTOR :
>>> The uncountable number does not have the 2nd digit of the 2nd
>>> countable number.
>>>
>>> UTM(neN,d) :
>>> ALL 10 digits are present in the 2nd digit position (following every
>>> possibility of the 1st digit) for an infinite number of reals.
>>>
>>> CANTOR :
>>> The uncountable number does not have the 3rd digit of the 3rd
>>> countable number.
>>> ...
>>>
>>>
>>> Start looking at reality sci.math not your text, not David Ullrich and
>>> Barb Knox who *make money teaching texts*. 0.123... is on the list of
>>> computable numbers infinite times with infinite possible tails after
>>> the 123. 0.654... is there infinite times. ALL PREFIXES of UNLIMITED
>>> LENGTH are ON THE LIST. You ----=== C A N N O T ===--- generate a
>>> new sequence of digits that is not on the list of computable reals.
>>> ALL PERMUTATIONS ARE THERE. The diag number must be SOME sequence of
>>> digits, like 0.123..., like 0.654... ITS NOT A NEW NUMBER, the elves
>>> went on strike!
>>
>> [snip]
>>
>> Where is THE LIST?
>>
>> David Bernier
>
>Not to mention HERC777's understanding.
It certainly is true that his understanding of Cantor's diagonal proof
is flawed.
Cantor proves that a list, making all the real numbers correspond to the
counting integers, is not possible, by showing that one can construct a
new number not on any such list by picking a number which differs in the
N-th place from the N-th element on the list.
Yes, it may well be that this different number will be in the N-th place
for *other* numbers on the list, but that is not the point.
You can create a list that makes all the rational numbers correspond to
the counting integers, or all the computable reals correspond to the
counting integers. You can create a list, therefore, that contains
elements which begin with any finite sequence of digits, however large.
Cantor's proof only works because the number of digits in the expansion
of a real number is *an actual completed infinity*; some real numbers
have infinitely complex descriptions, and are therefore both
uncomputable and unnameable.
Anyways, this will soon come to an end. Having been 11 years old some
years ago, our indefatigable poster will eventually become interested in
girls and leave us alone.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
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