• #### General Undecidable Axiom(2021 WIJ)

From wij@21:1/5 to All on Sat Jul 10 18:54:41 2021
Since the conventional HP only mentions a specific halting problem, which is often believed to be an invalid proof.

I hereby claims the General Undecidable Axiom(2021 WIJ): +--------------------------------------------------------------------------------+
| No TM U can decide the property of a TM P if that property can be defied by TM P. |
+--------------------------------------------------------------------------------+

// Example1:
// [Ret] true: f prints 'Y'
// false: f does not print 'Y'
bool U(Func f);

void P() {
if(U(P)) {
printf("b");
} else {
printf("Y");
}
}
//---

// Example2:
// [Ret] true: f is a "pathological self-reference" function
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
return;
} else {
P(); // if "pathological self-reference" is so defined, whatever.
}
};

------------------------
The construct of P (proof of General Undecidable Axiom) is 100% correct, intuitive and above all, REPRODUCIBLE, VERIFIABLE.

// [Ret] true: f has the (dynamic)property Q
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
// do whatever Q defines false
} else {
// do whatever Q defines
}
};

Note: I would like to acknowledge Olcott tirelessly refuted various conventional
HP proofs over these years. So I need not to do the same work again, though not necessary.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From wij@21:1/5 to wij on Sat Jul 31 04:12:21 2021
On Sunday, 11 July 2021 at 09:54:43 UTC+8, wij wrote:
Since the conventional HP only mentions a specific halting problem, which is often believed to be an invalid proof.

I hereby claims the General Undecidable Axiom(2021 WIJ): +--------------------------------------------------------------------------------+
| No TM U can decide the property of a TM P if that property can be defied by TM P. |
+--------------------------------------------------------------------------------+

// Example1:
// [Ret] true: f prints 'Y'
// false: f does not print 'Y'
bool U(Func f);

void P() {
if(U(P)) {
printf("b");
} else {
printf("Y");
}
}
//---

// Example2:
// [Ret] true: f is a "pathological self-reference" function
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
return;
} else {
P(); // if "pathological self-reference" is so defined, whatever.
}
};

------------------------
The construct of P (proof of General Undecidable Axiom) is 100% correct, intuitive and above all, REPRODUCIBLE, VERIFIABLE.

// [Ret] true: f has the (dynamic)property Q
// false: otherwise
bool U(Func f);

void P() {
if(U(P)) {
// do whatever Q defines false
} else {
// do whatever Q defines
}
};

Note: I would like to acknowledge Olcott tirelessly refuted various conventional
HP proofs over these years. So I need not to do the same work again, though not necessary.