Re: Different size infinities?

From: HERC777 (herc777_at_hotmail.com)
Date: 11/05/04

  • Next message: tchow_at_lsa.umich.edu: "Re: P vs NP craziness & Tim's interpretations" 
    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

  • Next message: tchow_at_lsa.umich.edu: "Re: P vs NP craziness & Tim's interpretations"

    Relevant Pages

    • Re: Different size infinities?
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