Re: Another proof: The Halting Problem Is Undecidable.

On Thu, 2024-10-10 at 22:43 +0800, wij wrote:

Axiom: Part is smaller than the whole.
 
Theorem: A system (physical device, computer,...) cannot compute/emulate a
         bigger system ... (like a computer cannot simulate a system (whatever)
         that contains it).
 
The concept is general. If applied to HP, H cannot compute the property (except
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
public are also fooled by Cantor's magic of infinite set: The set of even
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/RealNumber-zh.txt/download
and translated by Google Translator:
 
Appendix4: 2D-number can express plane. In 2D-number, as long as the distance
    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 should
    be expected. Inversely, exploring 'real number' by physics is basicly valid.
    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) the
    characteristics of the system containing it. Basically, it is the concept of
    "parts are smaller than the whole" (This is the definition). In addition,
    shutdown problems can also be explained by this concept. Cantor's infinite
    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 natural
    numbers". But, like the 0.999... problem, there is more than one 'set of
    natural numbers'. N<0,+2> = {0,2,4,6,..} can also be regarded as a set of
    natural numbers, in which 2,6,10,.. are odd numbers in N<0,+2>.
 
 

This "0.999...!=1" proof can also demonstrate the idea "Part is smaller the
 whole" from various kinds of instances:

 Expression B<1-A <=> B+A<1 always holds (Assume B=0.999.., A=the part to add to B):

 Ex: 0.9+0.09 < 1
     0.99+0.009 < 1
     0.999+0.0009 < 1
     ... (so on infinitely)
     0.999... < 1

 If "0.999...=1", the expression "B<1-A <=> A+B<1" does not hold.