Does everyone agree?
(1) We know that every software function invoked with the same data must have the same execution trace.
(1) We know that every software function invoked with the same data must have
the same execution trace.
(2) When a software function invokes itself this is recursive invocation.
(3) When the second recursive invocation of a software function calls itself with the same data as the prior invocation then it must have the same execution
trace as the prior invocation.
(4) When the second recursive invocation of a software function calls itself with the same data has no conditional branch instructions inbetween these two
invocations then this is a case of infinite recursion.
(5) When the recursive invocation is replaced with a call to a software system
that simulates the execution of the calling function with its same data, then
this is equivalent to a recursive invocation.
// P has address of H_Hat
void H_Hat(u32 P)
{
Simulate(P, P);
}
Does everyone agree?
(-1) In general for an algorithm or program to perform useful work its functions
contain branching logic.
(0) Only pure functions may not modify mutable state.
(1) We know that every software function invoked with the same data must have the same execution trace.
(2) When a software function invokes itself this is recursive invocation.
(3) When the second recursive invocation of a software function calls
itself with the same data as the prior invocation then it must have the
same execution trace as the prior invocation.
(4) When the second recursive invocation of a software function calls
itself with the same data has no conditional branch instructions
inbetween these two invocations then this is a case of infinite recursion.
(5) When the recursive invocation is replaced with a call to a software system that simulates the execution of the calling function with its
same data, then this is equivalent to a recursive invocation.
// P has address of H_Hat
void H_Hat(u32 P)
{
Simulate(P, P);
}
Does everyone agree?
(1) We know that every software function invoked with the same data must have the same execution trace.You took off all of this time to come up with this. Remember when you
(2) When a software function invokes itself this is recursive invocation.
(3) When the second recursive invocation of a software function calls
itself with the same data as the prior invocation then it must have the
same execution trace as the prior invocation.
(4) When the second recursive invocation of a software function calls
itself with the same data has no conditional branch instructions
inbetween these two invocations then this is a case of infinite recursion.
(5) When the recursive invocation is replaced with a call to a software system that simulates the execution of the calling function with its
same data, then this is equivalent to a recursive invocation.
// P has address of H_Hat
void H_Hat(u32 P)
{
Simulate(P, P);
}
Does everyone agree?
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.
Yes. The key brand new insight that I had about this proof is that the actual execution trace never reaches the undecidable portion, thus
making the conventional halting problem counter-examples {Linz, Sipser, Kozen} decidable.
// P has the machine address of H_Hat()
void H_Hat(u32 P)
{
u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
return;
}
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve >>> the halting problem for all possible program-input pairs cannot exist.
Yes. The key brand new insight that I had about this proof is that the
actual execution trace never reaches the undecidable portion, thus
The program has no "undecidable portion". We know perfectly well
whether it terminates or not, because it is trivial.
On 3/2/2021 11:46 AM, Kaz Kylheku wrote:
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve >>>> the halting problem for all possible program-input pairs cannot exist. >>>>
Yes. The key brand new insight that I had about this proof is that the
actual execution trace never reaches the undecidable portion, thus
The program has no "undecidable portion". We know perfectly well
whether it terminates or not, because it is trivial.
Daryl McCullough https://groups.google.com/g/comp.theory/c/wgJjJR78FaU/m/_eWPqsSS8bEJ
I can finally give credit where credit is due. Daryl McCullough was the
one that originally came up with this analogy in March of 2012.
When we ask Bill: Is your answer to this question "no" ?
Bill cannot possibly provide a correct answer because both answers of
"yes" and "no" form a contradiction.
The brand new insight that I documented that I came up with in 2016 was
that a halt decider that examines the simulation of its input as the
basis for its halting decision would never reach the point where it
returns any value to H_Hat().
On 3/2/2021 11:46 AM, Kaz Kylheku wrote:
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to
solve
the halting problem for all possible program-input pairs cannot exist. >>>>
Yes. The key brand new insight that I had about this proof is that the
actual execution trace never reaches the undecidable portion, thus
The program has no "undecidable portion". We know perfectly well
whether it terminates or not, because it is trivial.
You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:
Will Jack's answer to this question be no?
Jack can't possibly give a correct yes/no answer to the question.
In this same way Halts() cannot possibly provide a correct return value indicating halting / non halting to H_Hat().
// P has the machine address of H_Hat()
void H_Hat(u32 P)
{
u32 Input_Halts = Halts2(P, P);
if (Input_Halts)
HERE: goto HERE;
return;
}
The brand new insight that I documented that I came up with in 2016 was
that a halt decider that examines the simulation of its input as the
basis for its halting decision would never reach the point where it
returns any value to H_Hat().
On 3/2/2021 1:00 PM, olcott wrote:
On 3/2/2021 11:46 AM, Kaz Kylheku wrote:
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to
solve
the halting problem for all possible program-input pairs cannot exist. >>>>>
Yes. The key brand new insight that I had about this proof is that the >>>> actual execution trace never reaches the undecidable portion, thus
The program has no "undecidable portion". We know perfectly well
whether it terminates or not, because it is trivial.
There is a much earlier attribution to the same person:
sci.logic Daryl McCullough June 25, 2004
On Friday, June 25, 2004 at 6:30:39 PM UTC-5, Daryl McCullough wrote:
You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:
Will Jack's answer to this question be no?
Jack can't possibly give a correct yes/no answer to the question.
https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ
Jack cannot possibly provide a correct answer because both answers of
"yes" and "no" form a contradiction.
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 1:00 PM, olcott wrote:
On 3/2/2021 11:46 AM, Kaz Kylheku wrote:
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:
On 3/2/2021 10:36 AM, Otto J. Makela wrote:
I'm a bit late to the discussion, but this sounds a lot like you're >>>>>> trying to overturn Turing's proof that that a general algorithm to >>>>>> solve
the halting problem for all possible program-input pairs cannot exist. >>>>>>
Yes. The key brand new insight that I had about this proof is that the >>>>> actual execution trace never reaches the undecidable portion, thus
The program has no "undecidable portion". We know perfectly well
whether it terminates or not, because it is trivial.
There is a much earlier attribution to the same person:
sci.logic Daryl McCullough June 25, 2004
On Friday, June 25, 2004 at 6:30:39 PM UTC-5, Daryl McCullough wrote:
You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:
Will Jack's answer to this question be no?
Jack can't possibly give a correct yes/no answer to the question.
https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ
Jack cannot possibly provide a correct answer because both answers of
"yes" and "no" form a contradiction.
What you're perpetually missing is that a mathematical or
computatational function isn't Jack. If it gives a "yes" answer for some input, it can give no other answer. Functions don't have the choice of re-evaluating their answer and changing it.
Much of your rhetoric in this direction is laced with
anthropomorphic fallacy.
If we edit a function to give a different answer for the same input,
we are creating a different function. Since the input is the function
itself, the input has changed too!
You continue to be confused by this point; your work history consists
of producing different versions of code under the same names, taking different inputs under the same name, and speaking about it in terms as
if they are all one thing.
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:[more of the same]
Kaz Kylheku <563-365-8930@kylheku.com> writes:
On 2021-03-02, olcott <NoOne@NoWhere.com> wrote:[more of the same]
Kaz, olcott's article to which you replied was posted to
comp.theory, comp.lang.c, comp.lang.c++, and comp.software-eng,
with followups directed to comp.lang.c. Your followup ignored the >"Followup-To: comp.theory" header line and cross-posted to all
four newsgroups.
Is your newsreader buggy, or are you deliberately making
inappropriate cross-posts, or is something else going on?
I've cross-posted this article and set followups to comp.theory only.
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.
In comp.lang.c++ Otto J. Makela <om@iki.fi> wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.
If the halting problem could be solved, it would be great news for mathematics. Pretty much all unsolved problems in mathematics, at least
those that can be computed with an algorithm, would be solved in one
fell swoop.
The Riemann hypothesis? Simply create a program that checks every
single non-trivial zero of the zeta function and stops when it finds
one that's not on the critical line. Then simply use the marvelous
halting problem solution above to see if it ever terminates, and
you'll have proven the Riemann hypothesis as true or false.
Do odd perfect numbers exist? Simply create a program that goes
through every odd number and checks if it's perfect, and terminates
when it finds one. Use the halting problem proof to check if it will
ever terminate and you'll have solved the problem.
Collatz conjecture? Same thing. And so on and so forth.
I think Pete Olcott already said that he was not a mathematician. So
that means he is not constrained by such simple mathematical logic, and
can solve the impossible in an way that mathematicians cannot.
You know, in the same way that non-physicists are not constrained by
physical laws that they don't understand, and can thus make moon rockets
in their garage powered by gravity-repulsive paint.
David Brown <david.brown@hesbynett.no> wrote:
I think Pete Olcott already said that he was not a mathematician. So
that means he is not constrained by such simple mathematical logic, and
can solve the impossible in an way that mathematicians cannot.
You know, in the same way that non-physicists are not constrained by
physical laws that they don't understand, and can thus make moon rockets
in their garage powered by gravity-repulsive paint.
I haven't followed what he has written and said about his approach, but
if I were to guess, he's probably doing the same thing as so many other >pseudomathematicians do with such things, when trying to contradict >well-established corroborated mathematical proofs: Simply *redefine*
the original problem so that it (possibly) fits his "proof".
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
David Brown <david.brown@hesbynett.no> wrote:
I think Pete Olcott already said that he was not a mathematician. So
that means he is not constrained by such simple mathematical logic, and
can solve the impossible in an way that mathematicians cannot.
You know, in the same way that non-physicists are not constrained by
physical laws that they don't understand, and can thus make moon rockets
in their garage powered by gravity-repulsive paint.
I haven't followed what he has written and said about his approach, but
if I were to guess, he's probably doing the same thing as so many other pseudomathematicians do with such things, when trying to contradict well-established corroborated mathematical proofs: Simply *redefine*
the original problem so that it (possibly) fits his "proof".
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life >>>example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well
be defined, and computed to an arbitrary accuracy, using a finite >description.
03.03.2021 11:11 mickspud@potatofield.co.uk kirjutas:
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
You are confusing "definable" with "exactly representable in my favorite >notation".
The value of pi can be defined with no problems, and it can be also >represented exactly. The most common exact representation makes use of a >Greek letter.
On Wed, 3 Mar 2021 11:53:57 +0200
Paavo Helde <myfirstname@osa.pri.ee> wrote:
03.03.2021 11:11 mickspud@potatofield.co.uk kirjutas:
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
You are confusing "definable" with "exactly representable in my favorite
notation".
It would appear you are confusing definable with representable. Infinity
can be represented, that doesn't mean it can be defined especially given there are numerous different types.
The value of pi can be defined with no problems, and it can be also
represented exactly. The most common exact representation makes use of a
Greek letter.
I don't think you understand the meaning of an irrational number.
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well
be defined, and computed to an arbitrary accuracy, using a finite
description.
You really are an aspie arn't you. You can't even spot a light heated remark when its signposted with a smiley.
But if you want to be pedantic irrational numbers cannot be represented by the ratio of 2 integers therefor their true value is unknown and always will be.
On Wed, 3 Mar 2021 11:53:57 +0200
Paavo Helde <myfirstname@osa.pri.ee> wrote:
03.03.2021 11:11 mickspud@potatofield.co.uk kirjutas:
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
You are confusing "definable" with "exactly representable in my favorite
notation".
It would appear you are confusing definable with representable.
Infinity
can be represented, that doesn't mean it can be defined especially given there are numerous different types.
The value of pi can be defined with no problems, and it can be also
represented exactly. The most common exact representation makes use of a
Greek letter.
I don't think you understand the meaning of an irrational number.
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of >>>>squaring the circle becomes correct. (This is an actual real-life >>>>example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well
be defined, and computed to an arbitrary accuracy, using a finite >>description.
You really are an aspie arn't you. You can't even spot a light heated remark when its signposted with a smiley.
But if you want to be pedantic irrational numbers cannot be represented by the ratio of 2 integers therefor their true value is unknown and always will be.
On 03/03/2021 10:56, mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well
be defined, and computed to an arbitrary accuracy, using a finite
description.
You really are an aspie arn't you. You can't even spot a light heated remark >> when its signposted with a smiley.
A smiley works to indicate a joke like this when it is clear that the
poster knows that what they are writing is obviously and completely wrong.
But if you want to be pedantic irrational numbers cannot be represented by >> the ratio of 2 integers therefor their true value is unknown and always will >> be.
However, when you write this is is clear that you are not very familiar
with the mathematics at this level. (Nothing wrong with that, of course
- few people know or care what in means to be "computable".) The true
value of π is known - it is π. It can't be written as a finite decimal
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of >>>>>squaring the circle becomes correct. (This is an actual real-life >>>>>example.)
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well
be defined, and computed to an arbitrary accuracy, using a finite >>>description.
You really are an aspie arn't you. You can't even spot a light heated remark >> when its signposted with a smiley.
There is no joke in your statement. It's an assertion with no punchline
or anything. And it's an incorrect assertion.
Pi is a computable number, and therefore it's perfectly well definable.
On Wed, 3 Mar 2021 11:48:12 +0100[...]
David Brown <david.brown@hesbynett.no> wrote:
On 03/03/2021 10:56, mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
Strictly speaking pi is an irrational number so doesn't actually have >>>>> a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well >>>> be defined, and computed to an arbitrary accuracy, using a finite
description.
You really are an aspie arn't you. You can't even spot a light heated remark
when its signposted with a smiley.
A smiley works to indicate a joke like this when it is clear that the
poster knows that what they are writing is obviously and completely wrong.
Ok, define the value of Pi then. And I don't mean just C/D.
On Wed, 3 Mar 2021 11:48:12 +0100
David Brown <david.brown@hesbynett.no> wrote:
On 03/03/2021 10:56, mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 09:39:03 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
A bit like trying to redefine the value of pi so that a proof of
squaring the circle becomes correct. (This is an actual real-life
example.)
Strictly speaking pi is an irrational number so doesn't actually have >>>>> a definable value in the first place :)
Of course it does. Pi is a computable number, so it can perfectly well >>>> be defined, and computed to an arbitrary accuracy, using a finite
description.
You really are an aspie arn't you. You can't even spot a light heated remark
when its signposted with a smiley.
A smiley works to indicate a joke like this when it is clear that the
poster knows that what they are writing is obviously and completely wrong.
Ok, define the value of Pi then. And I don't mean just C/D.
But if you want to be pedantic irrational numbers cannot be represented by >>> the ratio of 2 integers therefor their true value is unknown and always will
be.
However, when you write this is is clear that you are not very familiar
with the mathematics at this level. (Nothing wrong with that, of course
So you are, good, then see above. Off you go...
- few people know or care what in means to be "computable".) The true
value of π is known - it is π. It can't be written as a finite decimal
It can't be written as a finite expansion in any number base and a symbol
is not a value - its a symbol.
On Wed, 3 Mar 2021 11:53:57 +0200
Paavo Helde <myfirstname@osa.pri.ee> wrote:
03.03.2021 11:11 mickspud@potatofield.co.uk kirjutas:
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
You are confusing "definable" with "exactly representable in my favorite >>notation".
It would appear you are confusing definable with representable. Infinity
can be represented, that doesn't mean it can be defined especially given there are numerous different types.
Thank you for proving my point so emphatically and also proving that you don't know what "light hearted" means. But then English is a 2nd or 3rd language for you so fair enough.
Pi is a computable number, and therefore it's perfectly well definable.
Define it then.
On Wed, 3 Mar 2021 11:16:47 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
Pi is a computable number, and therefore it's perfectly well definable.
Define it then.
mickspud@potatofield.co.uk wrote:
Thank you for proving my point so emphatically and also proving that you
don't know what "light hearted" means. But then English is a 2nd or 3rd
language for you so fair enough.
And assholery seems to be your first language.
Pi is a computable number, and therefore it's perfectly well definable.
Define it then.
It's the ratio between the circumference and the diameter of a circle.
Maybe you don't understand what a "definable number" is.
https://en.wikipedia.org/wiki/Definable_real_number
On Wed, 3 Mar 2021 12:41:33 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Thank you for proving my point so emphatically and also proving that you >>> don't know what "light hearted" means. But then English is a 2nd or 3rd >>> language for you so fair enough.
And assholery seems to be your first language.
Its spelt arsehole in England - the clue is in the name of the language. If I wanted to learn proper Finnish I wouldn't go to Sweden.
Pi is a computable number, and therefore it's perfectly well definable.
Define it then.
It's the ratio between the circumference and the diameter of a circle.
Maybe you don't understand what a "definable number" is.
https://en.wikipedia.org/wiki/Definable_real_number
I guess its a case of defining define.
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 12:41:33 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Thank you for proving my point so emphatically and also proving that you >>>> don't know what "light hearted" means. But then English is a 2nd or 3rd >>>> language for you so fair enough.
And assholery seems to be your first language.
Its spelt arsehole in England - the clue is in the name of the language. If I
wanted to learn proper Finnish I wouldn't go to Sweden.
And then you call me an "aspie".
I guess its a case of defining define.
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
On 03/03/2021 08:23, Juha Nieminen wrote:
In comp.lang.c++ Otto J. Makela <om@iki.fi> wrote:
I'm a bit late to the discussion, but this sounds a lot like you're
trying to overturn Turing's proof that that a general algorithm to solve >>> the halting problem for all possible program-input pairs cannot exist.
If the halting problem could be solved, it would be great news for
mathematics. Pretty much all unsolved problems in mathematics, at least
those that can be computed with an algorithm, would be solved in one
fell swoop.
The Riemann hypothesis? Simply create a program that checks every
single non-trivial zero of the zeta function and stops when it finds
one that's not on the critical line. Then simply use the marvelous
halting problem solution above to see if it ever terminates, and
you'll have proven the Riemann hypothesis as true or false.
Do odd perfect numbers exist? Simply create a program that goes
through every odd number and checks if it's perfect, and terminates
when it finds one. Use the halting problem proof to check if it will
ever terminate and you'll have solved the problem.
Collatz conjecture? Same thing. And so on and so forth.
I think Pete Olcott already said that he was not a mathematician. So
that means he is not constrained by such simple mathematical logic, and
can solve the impossible in an way that mathematicians cannot.
You know, in the same way that non-physicists are not constrained by
physical laws that they don't understand, and can thus make moon rockets
in their garage powered by gravity-repulsive paint.
On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
A computation that would not halt if its simulation were not
halted is indeed a non-halting computation.
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 11:53:57 +0200
Paavo Helde <myfirstname@osa.pri.ee> wrote:
03.03.2021 11:11 mickspud@potatofield.co.uk kirjutas:
Strictly speaking pi is an irrational number so doesn't actually have
a definable value in the first place :)
You are confusing "definable" with "exactly representable in my favorite >>> notation".
It would appear you are confusing definable with representable. Infinity
can be represented, that doesn't mean it can be defined especially given
there are numerous different types.
Maybe you should specify what you mean by "definable".
The number pi can certainly be defined in a completely unambiguous way
with a finite expression. Just because it may have an infinite non-recurring decimal expansion doesn't mean it can't be defined.
https://en.wikipedia.org/wiki/Definable_real_number
There exist real numbers that cannot be defined (with a finite expression), and in fact almost all real numbers are like that, but pi is not one
of them.
On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
A computation that would not halt if its simulation were not
halted is indeed a non-halting computation.
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
I think you are making stuff up as you go.
Juha Nieminen <nospam@thanks.invalid> writes:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
I think you are making stuff up as you go.
I think he's making stuff up that has even less to do with C++ than the original topic of this thread. I suggest not replying.
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
I think you are making stuff up as you go.
Juha Nieminen <nospam@thanks.invalid> writes:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
I think you are making stuff up as you go.
I think he's making stuff up that has even less to do with C++ than the >original topic of this thread. I suggest not replying.
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
I think you are making stuff up as you go.
As I've said before, English is not your first language so I won't blame you for not following everything.
On 04/03/2021 10:23, mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
That is not what it would mean to a mathematician. It's good enough, >perhaps, for a lot school maths. At a higher level, the term "number"
can be dependent on the context. /You/ probably just mean "decimal
digit", judging by your comment here. But to anyone interested in >mathematics beyond school level, "number" will usually mean "real
number" unless context dictates something else (integer, complex number, >transfinite number, length of a line, etc.).
As I've said before, English is not your first language so I won't blame you >> for not following everything.
Juha's written English is more accurate than yours. I believe I could
point out a dozen (minor) errors in the spelling and grammar of your
posts in this thread - I'm not sure I could find any in Juha's posts.
It would certainly be petty of me to do so, but hopefully you can see
the inappropriateness of railing on Juha's language skills.
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
I think you are making stuff up as you go.
As I've said before, English is not your first language so I won't blame you for not following everything.
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
You can't write the entire decimal expansion of 1/3.
On Thu, 4 Mar 2021 13:56:37 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
You can't write the entire decimal expansion of 1/3.
At the risk of getting drawn into this - the expansion of 1/3 can easily be written in a number of bases since its rational number. An irrational number cannot be written down in ANY real base.
On Thu, 4 Mar 2021 13:56:37 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
You can't write the entire decimal expansion of 1/3.
At the risk of getting drawn into this - the expansion of 1/3 can easily be written in a number of bases since its rational number. An irrational number cannot be written down in ANY real base.
mickspud@potatofield.co.uk wrote:
On Wed, 3 Mar 2021 21:00:41 +0000 (UTC)
Juha Nieminen <nospam@thanks.invalid> wrote:
mickspud@potatofield.co.uk wrote:
Let me ask it this way: Why do you consider a fraction, like 1/3,
to be a definable number?
It has a quantifiable value.
What does that even mean?
It means it has a value that can be written down using actual numbers.
You can't write the entire decimal expansion of 1/3.
Consider *why* you think that you can, and then consider how is that different from, for example, sqrt(2) or pi.
(Hint: What you can do is give a description, a definition, an algorithm
to write arbitrarily many of the digits of the decimal expansion of
that number. The same is true for all three examples above.)
sqrt(2) and pi are not any less "well-defined" as 1/3 is. The exact
algorithm to print out arbitrarily many digits of their decimal expansion
may be a bit more complicated, but that means nothing in this context.
I think you are making stuff up as you go.
As I've said before, English is not your first language so I won't blame you >> for not following everything.
One has to wonder why you feel the need to be so arrogant and condescending.
Ironically, I think I know English better than you. At least I know what a "definable number" is.
No kindly shove your patronising attitude up your arse and fuck off.[...]
[...]
No kindly shove your patronising attitude up your arse and fuck off.[...]
Welcome to my killfile. I encourage others to do likewise.
Detecting and handling infinite recursion is easy:
__try
{
...
}
__except( GetExceptionCode() == EXCEPTION_STACK_OVERFLOW ? EXCEPTION_EXECUTE_HANDLER : EXCEPTION_CONTINUE_SEARCH )
{
...
}
Hrhr.
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