Re: Is this ℙ≠ℕℙ proof 'humiliating'?

On 10/06/2024 01:06, wij wrote:
[I wrote:]

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

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

[...]  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.

There is no reason at all why they should be the same.  Once you get
past the set of rationals, there are several ways mathematics could have gone
[and perhaps have gone on some remote planets].  Which way you choose makes
little difference to [eg] practical engineering, which can be approximated as
closely as you like using only rationals, but makes a huge difference (a) to
pedagogy and (b) to abstract theory [eg of infinity, computability, ...].

Honestly, I am not good in mathematics (I only read what I feel need to) but
seems good enough for my purpose.

Well, it's clearly /not/ good enough for that.  Perhaps if your real
purpose was explained better, people here or elsewhere could help you;  but
not if you refuse to put in the effort yourself, and instead keep repeating
the same wrong or ill-explained claims.

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.

Surreals and hyperreals are not at all the same.  But they both include
infinitesimals, which seem to be what you want.  If you could devote some of
the time you spend trying to patch up your previous work to studying [eg] the
surreals instead, you would surely make more progress.
[P ?= NP:]

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.

No, that's not the problem.  Ben's [and my] point is that whether or
not p [ie, whether or not a given integer is even] is NPC is /equivalent/ to
whether or not P == NP.  This is explained in any competent course in CS that
includes the topic of NP completeness.  You are assuming what you are trying
to prove.  Doing this once is the sort of mistake we all make from time to
time.  Doing it repeatedly after it has been explained to you suggests that
the next stage is to place your head on a piece of wood and thwack it with
another piece of wood until enlightenment dawns.
--
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Handel