Sujet : Re: Is this ℙ≠ℕℙ proof 'humiliating'?
De : wyniijj5 (at) *nospam* gmail.com (wij)
Groupes : comp.theoryDate : 10. Jun 2024, 15:26:39
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <7f6d7e92eef8b68407f931fd3242cdcc1cd946c1.camel@gmail.com>
References : 1 2 3 4
User-Agent : Evolution 3.50.2 (3.50.2-1.fc39)
On Mon, 2024-06-10 at 00:36 +0100, Ben Bacarisse wrote:
wij <wyniijj5@gmail.com> writes:
On Sun, 2024-06-09 at 20:55 +0100, Ben Bacarisse wrote:
wij <wyniijj5@gmail.com> writes:
ℙ≠ℕℙ
Proved. 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 p∉ℕℙℂ is a false proposition because all ℕℙ problems
including ℕℙℂ are mutually Ptime reducible. Since p∉ℕℙℂ is true,
ℙ≠ℕℙ is concluded.
Where is your proof that p is not NP-complete? Since you don't know
this subject very well, you would benefit more from asking people to
direct you to resources from which you could learn, rather than posting
provocative messages.
<silly insults deleted>
To be on topic, can you show us the p (as mentioned) is NPC or p is
not NPC, either will do, to prove how much you understand what you
talked about.
If I could do that I would be rich, quite literally. Sadly, I can't and
neither can anyone else on the planet (so far). But if you think you
can, head over to the Clay Mathematics Institute and persuade them to
give you a million dollars[1].
For the hard-of-understanding, a proof that p, which is obviously in P,
is also in NPC would immediately prove that P=NP. Alternatively, a
proof that p is not in NPC would immediately prove that P=/=NP.
[1] https://www.claymath.org/millennium/p-vs-np/
Probably I should make the Proof2 more formal:
If p∈ℕℙℂ, then ℙ=ℕℙ and the concept of ℕℙℂ is useless.
If p∉ℕℙℂ, then ℙ=ℕℙ will be a contradiction (leads to p∈ℕℙℂ), so ℙ≠ℕℙ is true in this case.
Summary: Because ℕℙℂ is considered not useless, therefore ℙ≠ℕℙ is concluded.