Re: Is this ℙ≠ℕℙ proof 'humiliating'?

On Sun, 2024-06-09 at 23:57 +0100, Andy Walker wrote:

On 09/06/2024 22:58, wij wrote:
[To Ben:]

Do you still insist 0.999...∉[0,1)? LOL.

 
Before anyone "insists" on either that or its contrary, you need
to explain your notation.  If you are talking about conventional "Real"
numbers, then the proof is straightforward and known to everyone with a
decent education in mathematics.  If you're talking about some different
"Wij-numbers", then no-one here can tell you what their properties are
until you define them properly, and your various attempts to do that over
the years have been long on assertions and short on axioms and proofs.
Adding "LOL" to everything you think you understand better than Ben is
unhelpful.  For my part, I can only repeat earlier suggestions that you
read up about "Surreal" and "Hyperreal" numbers [Wiki is your friend];
they solve many of the problems you seem to have with "Real" numbers.

Thanks to Richard Damon, I changed my goal to rectify "conventional real". I was
only interested in MY real but forced to deal with RD's real. Since by the end
, they should the same, so I took the challenge. 
Honestly, I am not good in mathematics (I only read what I feel need to) but 
seems good enough for my purpose.
Maybe I could see what "Surreal" ("Hyperreal" should be the same) solves and
see how my real can (must) solve that problem. But I don't have time for that.

   This time, suggesting you are very
knowledgeable that "Determine n is even" not NPC needs proof...LOL again.

 
Again, before you disrespect Ben, perhaps you should think about
what he said to you.  Generations of undergraduates have been asked what
they could deduce about NPC *if* P == NP.  In the light of that, your
assumption that your problem "p" is not NPC amounts to assuming P /= NP,
so it's not surprising [but is unhelpful] that P /= NP follows from it.
[Hint:  Think about how you could reduce an instance of some "difficult"
decision problem to a (trivial) instance of "p".]

My best guess is that the phrase in my proof is not clear. It had been modified
from the reply by immibis several days before.

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This file is intended a proof that ℙ≠ℕℙ. The contents may be updated anytime.
https://sourceforge.net/projects/cscall/files/MisFiles/PNP-proof-en.txt/download
...[cut]
   Proof2: Let p="Given a number n, determine whether or not n is even". If
          ℙ=ℕℙ, then all the existing proofs of p∉ℕℙℂ are false proofs (because
          all ℕℙ problems including ℕℙℂ will be mutually Ptime reducible). Since
          the proofs that p∉ℕℙℂ are true, ℙ≠ℕℙ is concluded.
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