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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Another proof: The Halting Problem Is Undecidable.
Date: Thu, 10 Oct 2024 22:43:52 +0800
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Axiom: Part is smaller than the whole.

Theorem: A system (physical device, computer,...) cannot compute/emulate a=
=20
         bigger system ... (like a computer cannot simulate a system (whate=
ver)
         that contains it).

The concept is general. If applied to HP, H cannot compute the property (ex=
cept
trivial) of D, simply because D contains (maybe logically) H as a part.

Thus, can the part equal to the whole? Definitely not, by definition. The=
=20
public are also fooled by Cantor's magic of infinite set: The set of even=
=20
number, say X, is actually a distinct set isomophic to the natural number (=
not
a part of it). The element in X is not 'even' in X.... Basically, there are=
 many
set of natural number, not just one. The set of 'natural number' has to be
explicitly specified to avoid ambiguity in discussion.

Snippet from https://sourceforge.net/projects/cscall/files/MisFiles/RealNum=
ber-zh.txt/download
and translated by Google Translator:

Appendix4: 2D-number can express plane. In 2D-number, as long as the distan=
ce
    postulate (1. Distance between points is invariant by movement 2.The
    ratio of distance between points is invariant by scalar multiplication)=
 are
    satisfied, Euclidean geometry system can be established. What is meant =
to
    say is that: Such a 'mass-point universe' is constructed based on our
    preset property. We are ultimately exploring the semantics of our own
    knowledge. And, as long as the logic holds, the respective reality shou=
ld
    be expected. Inversely, exploring 'real number' by physics is basicly v=
alid.
    In the digital era, universe (semantics) is a natural computer.
Appendix 5: ....
Appendix 6: From Appendix 4, it can be roughly concluded that: a system
    (physical device, computer, k,...etc.) cannot calculate (or simulate) t=
he
    characteristics of the system containing it. Basically, it is the conce=
pt of
    "parts are smaller than the whole" (This is the definition). In additio=
n,
    shutdown problems can also be explained by this concept. Cantor's infin=
ite
    set theory may lead to the fallacy that "parts are equal to the whole",
    such as "the number of even numbers is the same as the number of natura=
l
    numbers". But, like the 0.999... problem, there is more than one 'set o=
f
    natural numbers'. N<0,+2> =3D {0,2,4,6,..} can also be regarded as a se=
t of
    natural numbers, in which 2,6,10,.. are odd numbers in N<0,+2>.