Cantor's complete list assumption is not extrapolated
From: HERC777 (herc777_at_hotmail.com)
Date: 10/28/04
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Date: 28 Oct 2004 16:18:03 -0700
I'll borrow the word permutation to mean unique sequence.
1 Assume a real number list
2 Form a new permutation different to every number on the list
3 The list is incomplete
1 Assume a COMPLETE real number list containing every permutation
2 Form a new permutation different to every number on the list
3 CONTRADICTION - the list is already complete
The assumption 1, is that every infinitely long permutation is listed.
The anti-diag number is literally constructed as
"form a new permutation different to every number on the list".
With a finite list anti-diag always forms a new number and
is a valid technique, its easy to imagine an infinite anti-diag
but is it valid? It forms a contradiction so either 1 or 2 is wrong.
Given every infinite permutation is present on the list, the
*construction* of a new permutation is itself flawed.
A binary example.
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..
Each sample runs forever, there is unlimited sampling and
resources for the experiment. After about 10 samples, all
possible permutations for the 1st 3 frames are recorded.
000
001
010
011
100
101
110
111
8 possibilities, with some doubling up of results.
After several million samples, the variations in the first 15
frames are all covered.
000000000000000101010101010...
000000000000001101010101010...
000000000000010101010101010...
000000000000011101010101010...
..
111111111111111101010101010...
This process is logarithmic, it takes much longer for the
covered permutations to grow as the list grows. What is the
behaviour as the list approaches infinity?
log(oo) = 00
Do all permutations eventually occur? This is the expected
physical and probabilistic result. Using infinite diagonalisation
this theoretically does not happen, even with infinite resources.
There are infinite samples, all *known* permutations are covered
yet anti-diag results in a new permutation??
According to accepted mathematics today, the log(oo) length of
the covered permutations reaches an end, and the tail end of the
numbers are again random and unique.
This is what hyperinfinity is based on, the privaleged concept
all mathematicians understand beyond the man in the streets' reasoning.
ASSUME the list of permutations is complete, IT IS!
Construct the anti-diagonal, anti-diagonal is not unique
after 3 digits, its not unique after 15 digits, its not
unique after infinite digits, all permutations are present.
You have an INFINITE sample of radioactive readouts. Are you
100% absolutely certain you can find a new sequence of 1s and 0s?
Herc
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