Re: Yet another contribution to the P-NP question

On Thu, 2024-09-26 at 15:21 -0700, Keith Thompson wrote:

wij <wyniijj5@gmail.com> writes:
[...]

I think my proof have presentation problems as a formal proof, but the
goal is for myself only, so not a real problem for me (P-NP problem is
very tricky to prove, mightbe worse than the "0.999...==1" false
belief).
 
By the way, "repeating decimal is irrational" (because, in short,
statement "ℚ+ℚ=ℚ" only valid in finite steps of
application. ... Contemporary axiomatic system has a serious problem,
ALL EXISTING PROOFS or knowledge should be re-examined).

 
You've claimed before that 0.999... is not equal to 1, and that
repeating decimals are irrational.  You failed to answer my
straightforward questions about these beliefs.
 
I'll try one last time.
 
We are discussing the conventionally defined *real numbers*.  If you're
using some other number system please say so, and tell us what number
system you're using.  (There are a number of such systems, including
hypperreals and surreals.)
 
What exactly do you mean by "0.999..."?  What does the ellipsis notation
mean to you?  What it means to most of us is the *limit* as the number
of 9s increases without bound.  (I can write it in more rigorous
mathematical notation, but I probably won't bother.)  Does it mean the
same thing to you?
 
Do you understand what a *limit* is?  Do you understand that the limit
of a sequence might not be a member of the sequence?
 
I will consider continuing to discuss this with you if and only if you
provide coherent answers to these questions.

Sorry that I forgot what kind of "0.999... questions" were asked by who. The email
system (USENET) is difficult for me to find things in the post history.
To keep the post short (this is not a proper thread), this file
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/download
should answer your listed questions which I had disscussed many times in the
past and not willing to repeat them, of course, except there is someting new.