Re: Different size infinities?
From: HERC777 (herc777_at_hotmail.com)
Date: 11/04/04
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Date: 4 Nov 2004 15:00:38 -0800
No one has commented on my disproof of Cantors
diagonal technique.
Concise version:
2 differently programmed (1) Universal Turing Machines
output reals for each of the integers in sequence.
UTM1(n) neN
UTM2(n) neN
Diagonalisation is used on UTM1 to find a new real not
in UTM1's output.
By the Church Turing Thesis, UTM2 is the same set of reals
as UTM1, no computing system can compute anything that
any other Turing compatible computing sytem cannot.
Yet the new number is a member of UTM2 and not UTM1.
CONTRADICTION
Therefore, the diagonalisation step is erronous.
(1) there is no possible algorithm to tranform any program of
UTM1 to UTM2 or vice versa, the set/sequence of reals they
produce are independant.
Then try to answer this question which puts uncountable infinity
supporters in an obsurd situation.
>
> Small samples of radioactive material have their particle emission
> rate measured. A sample frame rate is established and the output
> of a digitised poisson distribution is recorded, 0 for no emission,
> 1 for a particle emmitted - a ping on the gieger counter.
>
> sample 1 0101010010010100101010110111010101010..
> sample 2 010101011010101010101010101010101010..
> sample 3 1110110101110101011101011010101101010..
>
> After several million samples, the variations in the first 15
> frames are all covered.
>
000000000000000101010101010...
000000000000001101010101010...
000000000000010101010101010...
000000000000011101010101010...
..
111111111111111101010101010...
----------------->
all permutations
the size of all permutations covered tends to oo as the
size of the list -> oo.
> You have INFINITE samples with radioactivity readouts. Are you
> 100% certain you can find a new sequence of 1s and 0s?
>
Herc
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