On 6/5/22 12:39 PM, olcott wrote:
> On 6/5/2022 11:31 AM, Richard Damon wrote:
>> On 6/5/22 11:57 AM, olcott wrote:
>>> On 6/5/2022 7:38 AM, Ben wrote:
>>>> Alan Mackenzie <acm@muc.de> writes:
>>>>
>>>>> olcott <NoOne@nowhere.com> wrote:
>>>>>> On 6/5/2022 6:12 AM, Alan Mackenzie wrote:
>>>>
>>>>>>> ...  What would be the turing machine equivalent of an
>>>>>>> "abnormal termination" in C?
>>>>>
>>>>>> An aborted simulation.
>>>>>
>>>>> There's no such thing on a turing machine.  It either runs and
>>>>> halts, or
>>>>> it runs forever.
>>>>>
>>>>> Your aborted simulation is just one final state of a turing machine,
>>>>> which has thus halted.
>>>>
>>>> A year ago I tried to get PO to accept a few basic facts about the
>>>> topic.  One of these was
>>>>
>>>> (B) Every computation that halts, for whatever reason, is a halting
>>>>      computation.
>>>>
>>>> After much ducking a diving, PO replied "OK".
>>>>
>>>
>>> Whatever I said years ago has been superseded by my current
>>> understanding:
>>>
>>> Computation that halts ... the Turing machine will halt whenever it
>>> enters a final state. (Linz:1990:234)
>>>
>>>
>>
>> And H^ applied to <H^> will Halt if H applied to <H^> <H^> rejects its
>> input as non-halting, thus showing that the H was wrong.
>
> You are a brain dead moron on this point.
>
>

Why, for speaking Truth that you can't counter?

Your problem is that you use inconsistent logic and twisted definitions.

When you actually are forced to state definitions (accepted by the
field), they show that your logic is just wrong.

On 6/5/2022 11:56 AM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:50:13 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:28 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:22:45 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>
>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>> exact value.
>>>>>>
>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>> finite terms in some particular representation is quite
>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>> standard decimals is merely one [common] choice. Note that in
>>>>>>>> symbolic computer systems, those computable reals are
>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>> rationals equally have no terminating expansion. Numbers such
>>>>>>>> as "pi" and "sqrt(2)" are not defined as decimal expansions
>>>>>>>> but via their properties [eg that "sqrt(2)" is the unique
>>>>>>>> positive real whose square is 2, or equivalently that it is
>>>>>>>> the ratio of the diagonal of a square to its side, and "pi" is
>>>>>>>> the least positive real whose sine is zero]. Those properties
>>>>>>>> are exact, and tell you all you ever need to know about those
>>>>>>>> numbers.
>>>>>>
>>>>>> [ .... ]
>>>>>>
>>>>>>> What has decimal (base 10) expansion got to do with anything? An
>>>>>>> irrational number has a non-terminating sequence in ANY base. I
>>>>>>> am sorry but you are simply mistaken: irrational numbers do NOT
>>>>>>> have an exact value; this is obvious to anyone who understands
>>>>>>> logic and uses a sane definition for infinity.
>>>>>>
>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>> there are many) have nothing to do with this.
>>>>>
>>>>> You are wrong and fractally so so your degree in maths appears to
>>>>> be worthless. An irrational number's sequence is statistically
>>>>> random, has no fixed point on the number line ergo has no exact
>>>>> representation. Any number with no exact representation has, by
>>>>> definition, no exact value, only an approximation. Infinity has
>>>>> everything to do with this as an irrational's sequence ("digits")
>>>>> never terminates (i.e. it is an INFINITELY long sequence).
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Nope. Irrational numbers DO have exact points on the number line.
>>>>
>>>> And what does representation have to do with exact value?
>>>>
>>>> Also, irrational numbers sequence of digits are not necessarily
>>>> statistically random, in some representations, they can be VERY
>>>> predictible for some numbers.
>>>>
>>>> One simple construction to show exact position, draw a box with
>>>> sides exactly 1.
>>>>
>>>> Draw a line though opposite corners and make one point the value 0.
>>>>
>>>> The other corner will be EXACTLY at the point sqrt(2), so that
>>>> irrational number has an exact point on the number line.
>>>>
>>>> You just don't understand what an exact value means, likely because
>>>> you can't understand things that are somewhat abstract.
>>>
>>> An irrational number does not have an exact point on the number
>>> line as it will move about as you "zoom in", you can keep "zooming
>>> in" forever (i.e. infinitely) and it will keep moving about because
>>> the number never terminates.
>>>
>>> If I couldn't understand things that are somewhat abstract then I
>>> wouldn't have a computer science degree (BSc Hons) and 30 years of
>>> industry experience.
>>>
>>> /Flibble
>>>
>>
>> Then why do you think irrational numbers don't have an exact location?
>>
>> I know people with degrees (even with honors) and industry experiance
>> that still show that they don't really understand what they are
>> talking about.
>>
>> The "width" of the point representing the location of an irrational
>> number is just as much "0" as that of a rational number, so specifies
>> just as exact of a location.
>>
>> The fact that we can't write it in a rational base with a finite
>> number of digits doesn't actally mean anything.
>
> 3.1415xxxxxxxxx (a)
> 3.14159xxxxxxxx (b)
>
> (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its value
> "moves about" as accuracy increases.
>
> /Flibble
>

You are confusing the representation of the number in decimal digits
with the actual number itself.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 6/5/2022 11:59 AM, Richard Damon wrote:
> On 6/5/22 12:39 PM, olcott wrote:
>> On 6/5/2022 11:31 AM, Richard Damon wrote:
>>> On 6/5/22 11:57 AM, olcott wrote:
>>>> On 6/5/2022 7:38 AM, Ben wrote:
>>>>> Alan Mackenzie <acm@muc.de> writes:
>>>>>
>>>>>> olcott <NoOne@nowhere.com> wrote:
>>>>>>> On 6/5/2022 6:12 AM, Alan Mackenzie wrote:
>>>>>
>>>>>>>> ...  What would be the turing machine equivalent of an
>>>>>>>> "abnormal termination" in C?
>>>>>>
>>>>>>> An aborted simulation.
>>>>>>
>>>>>> There's no such thing on a turing machine.  It either runs and
>>>>>> halts, or
>>>>>> it runs forever.
>>>>>>
>>>>>> Your aborted simulation is just one final state of a turing machine,
>>>>>> which has thus halted.
>>>>>
>>>>> A year ago I tried to get PO to accept a few basic facts about the
>>>>> topic.  One of these was
>>>>>
>>>>> (B) Every computation that halts, for whatever reason, is a halting
>>>>>      computation.
>>>>>
>>>>> After much ducking a diving, PO replied "OK".
>>>>>
>>>>
>>>> Whatever I said years ago has been superseded by my current
>>>> understanding:
>>>>
>>>> Computation that halts ... the Turing machine will halt whenever it
>>>> enters a final state. (Linz:1990:234)
>>>>
>>>>
>>>
>>> And H^ applied to <H^> will Halt if H applied to <H^> <H^> rejects
>>> its input as non-halting, thus showing that the H was wrong.
>>
>> You are a brain dead moron on this point.
>>
>>
>
> Why, for speaking Truth that you can't counter?

The actual truth is beyond your intellectual capacity on this point.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Mr Flibble <flibble@reddwarf.jmc> wrote:
> On Sun, 5 Jun 2022 16:34:18 -0000 (UTC)
> Alan Mackenzie <acm@muc.de> wrote:

>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>> > On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>> > Alan Mackenzie <acm@muc.de> wrote:

>> >> Mr Flibble <flibble@reddwarf.jmc> wrote:
>> >> > On Sun, 5 Jun 2022 16:28:05 +0100
>> >> > Andy Walker <anw@cuboid.co.uk> wrote:

>> >> >> On 05/06/2022 14:47, Mr Flibble wrote:
>> >> >> > On Sun, 5 Jun 2022 07:58:42 -0400
>> >> >> > Richard Damon <Richard@Damon-Family.org> wrote:
>> >> >> >> [...] Sort of like how the number Pi has an
>> >> >> >> exact value, but you can never actually express it (because
>> >> >> >> it takes an infinite number of digits).
>> >> >> > PI does not have an exact value; no irrational number has an
>> >> >> > exact value.

>> >> >> Of course "pi" has an exact value; as do [eg] "sqrt(2)", "e",
>> >> >> and all the other computable real [and complex] numbers.
>> >> >> Whether that value can be expressed in finite terms in some
>> >> >> particular representation is quite another matter. That in turn
>> >> >> depends on the representation; standard decimals is merely one
>> >> >> [common] choice. Note that in symbolic computer systems, those
>> >> >> computable reals are typically written "pi" [or whatever], and
>> >> >> the computer works with that exactly, so that [eg] "sin^2 (pi/3)
>> >> >> == 3/4", not 0.7499...; and also that in decimal-type notations
>> >> >> most rationals equally have no terminating expansion. Numbers
>> >> >> such as "pi" and "sqrt(2)" are not defined as decimal expansions
>> >> >> but via their properties [eg that "sqrt(2)" is the unique
>> >> >> positive real whose square is 2, or equivalently that it is the
>> >> >> ratio of the diagonal of a square to its side, and "pi" is the
>> >> >> least positive real whose sine is zero]. Those properties are
>> >> >> exact, and tell you all you ever need to know about those
>> >> >> numbers.

>> >> [ .... ]

>> >> > What has decimal (base 10) expansion got to do with anything? An
>> >> > irrational number has a non-terminating sequence in ANY base. I
>> >> > am sorry but you are simply mistaken: irrational numbers do NOT
>> >> > have an exact value; this is obvious to anyone who understands
>> >> > logic and uses a sane definition for infinity.

>> >> That irrational numbers are exact values is clear to anybody with a
>> >> degree in maths. Definitions of "infinity" (of which there are
>> >> many) have nothing to do with this.

>> > You are wrong and fractally so so your degree in maths appears to be
>> > worthless.

>> No, I am right, along with the world's other mathematics graduates.
>> You are stuck in the distant (100s of years) past, when mathematicians
>> were still puzzling over what you're puzzling over. The fundamentals
>> of maths have been worked out, and you are in the position of an
>> alchemist faced with modern chemistry.

> Pure assertion with NOTHING to back it up.

I have several years of hard study to back it up, combined with the
authority of the world's mathematicians. If you were to insist the world
were flat rather than roughly a sphere, and I were to correct you, I
would likewise have "nothing to back it up". But you would still be
wrong. Why do you have so little respect for education?

You make the mistake of thinking that because everybody is free to hold
opinions, everybody's opinion is equally valid. This is untrue -
experts' expertise is worth far more than the opinionated peoples'
opinions.

>> > An irrational number's sequence is statistically random, has no
>> > fixed point on the number line ergo has no exact representation.
>> > Any number with no exact representation has, by definition, no
>> > exact value, only an approximation. Infinity has everything to do
>> > with this as an irrational's sequence ("digits") never terminates
>> > (i.e. it is an INFINITELY long sequence).

> Ignored this part I see.

Yes. It is so full of errors, misunderstandings of definitions, and
general lack of education, it is hardly worth countering. You don't know
what a real number is, for example. You don't know the axioms by which
the properties of numbers have been established. You don't know how
these numbers are constructed. And were I to spend several weeks and
months trying to get these points across to you, in the end you might
well just chose to stay ignorant. I've got better things to do with my
time.

> /Flibble

--
Alan Mackenzie (Nuremberg, Germany).

On 6/5/22 12:56 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:50:13 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:28 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:22:45 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>
>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>> exact value.
>>>>>>
>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>> finite terms in some particular representation is quite
>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>> standard decimals is merely one [common] choice. Note that in
>>>>>>>> symbolic computer systems, those computable reals are
>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>> rationals equally have no terminating expansion. Numbers such
>>>>>>>> as "pi" and "sqrt(2)" are not defined as decimal expansions
>>>>>>>> but via their properties [eg that "sqrt(2)" is the unique
>>>>>>>> positive real whose square is 2, or equivalently that it is
>>>>>>>> the ratio of the diagonal of a square to its side, and "pi" is
>>>>>>>> the least positive real whose sine is zero]. Those properties
>>>>>>>> are exact, and tell you all you ever need to know about those
>>>>>>>> numbers.
>>>>>>
>>>>>> [ .... ]
>>>>>>
>>>>>>> What has decimal (base 10) expansion got to do with anything? An
>>>>>>> irrational number has a non-terminating sequence in ANY base. I
>>>>>>> am sorry but you are simply mistaken: irrational numbers do NOT
>>>>>>> have an exact value; this is obvious to anyone who understands
>>>>>>> logic and uses a sane definition for infinity.
>>>>>>
>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>> there are many) have nothing to do with this.
>>>>>
>>>>> You are wrong and fractally so so your degree in maths appears to
>>>>> be worthless. An irrational number's sequence is statistically
>>>>> random, has no fixed point on the number line ergo has no exact
>>>>> representation. Any number with no exact representation has, by
>>>>> definition, no exact value, only an approximation. Infinity has
>>>>> everything to do with this as an irrational's sequence ("digits")
>>>>> never terminates (i.e. it is an INFINITELY long sequence).
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Nope. Irrational numbers DO have exact points on the number line.
>>>>
>>>> And what does representation have to do with exact value?
>>>>
>>>> Also, irrational numbers sequence of digits are not necessarily
>>>> statistically random, in some representations, they can be VERY
>>>> predictible for some numbers.
>>>>
>>>> One simple construction to show exact position, draw a box with
>>>> sides exactly 1.
>>>>
>>>> Draw a line though opposite corners and make one point the value 0.
>>>>
>>>> The other corner will be EXACTLY at the point sqrt(2), so that
>>>> irrational number has an exact point on the number line.
>>>>
>>>> You just don't understand what an exact value means, likely because
>>>> you can't understand things that are somewhat abstract.
>>>
>>> An irrational number does not have an exact point on the number
>>> line as it will move about as you "zoom in", you can keep "zooming
>>> in" forever (i.e. infinitely) and it will keep moving about because
>>> the number never terminates.
>>>
>>> If I couldn't understand things that are somewhat abstract then I
>>> wouldn't have a computer science degree (BSc Hons) and 30 years of
>>> industry experience.
>>>
>>> /Flibble
>>>
>>
>> Then why do you think irrational numbers don't have an exact location?
>>
>> I know people with degrees (even with honors) and industry experiance
>> that still show that they don't really understand what they are
>> talking about.
>>
>> The "width" of the point representing the location of an irrational
>> number is just as much "0" as that of a rational number, so specifies
>> just as exact of a location.
>>
>> The fact that we can't write it in a rational base with a finite
>> number of digits doesn't actally mean anything.
>
> 3.1415xxxxxxxxx (a)
> 3.14159xxxxxxxx (b)
>
> (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its value
> "moves about" as accuracy increases.
>
> /Flibble
>

But (a) and (b) aren't "pi"

All you are showing is that approximations to numbers get better as they
get better, which is just a strange tautology.

The number PI, has only one precise value, the exact ratio of the
circumference of a circle to its diameter on a flat plane (which will
always be the same).

The fact that it can't be expressed, isn't an issue on exactness, but of
finite representation.

Note, that the set of numbers with finite representation is a countable
set, so it isn't surprising that the uncountable infinity of the reals
(that includes the irrationals) is not all finitely expressible.

On 6/5/22 12:58 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:54:22 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:42 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 11:41:05 -0500
>>> olcott <NoOne@NoWhere.com> wrote:
>>>
>>>> On 6/5/2022 11:38 AM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 16:34:18 -0000 (UTC)
>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>
>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>
>>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>>>> exact value.
>>>>>>
>>>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>>>> finite terms in some particular representation is quite
>>>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>>>> standard decimals is merely one [common] choice. Note that
>>>>>>>>>> in symbolic computer systems, those computable reals are
>>>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>>>> rationals equally have no terminating expansion. Numbers such
>>>>>>>>>> as "pi" and "sqrt(2)" are not defined as decimal expansions
>>>>>>>>>> but via their properties [eg that "sqrt(2)" is the unique
>>>>>>>>>> positive real whose square is 2, or equivalently that it is
>>>>>>>>>> the ratio of the diagonal of a square to its side, and "pi"
>>>>>>>>>> is the least positive real whose sine is zero]. Those
>>>>>>>>>> properties are exact, and tell you all you ever need to know
>>>>>>>>>> about those numbers.
>>>>>>
>>>>>>>> [ .... ]
>>>>>>
>>>>>>>>> What has decimal (base 10) expansion got to do with anything?
>>>>>>>>> An irrational number has a non-terminating sequence in ANY
>>>>>>>>> base. I am sorry but you are simply mistaken: irrational
>>>>>>>>> numbers do NOT have an exact value; this is obvious to anyone
>>>>>>>>> who understands logic and uses a sane definition for
>>>>>>>>> infinity.
>>>>>>
>>>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>>>> there are many) have nothing to do with this.
>>>>>>
>>>>>>> You are wrong and fractally so so your degree in maths appears
>>>>>>> to be worthless.
>>>>>>
>>>>>> No, I am right, along with the world's other mathematics
>>>>>> graduates. You are stuck in the distant (100s of years) past,
>>>>>> when mathematicians were still puzzling over what you're
>>>>>> puzzling over. The fundamentals of maths have been worked out,
>>>>>> and you are in the position of an alchemist faced with modern
>>>>>> chemistry.
>>>>>
>>>>> Pure assertion with NOTHING to back it up.
>>>>>
>>>>>>
>>>>>>> An irrational number's sequence is statistically random, has no
>>>>>>> fixed point on the number line ergo has no exact representation.
>>>>>>> Any number with no exact representation has, by definition, no
>>>>>>> exact value, only an approximation. Infinity has everything to
>>>>>>> do with this as an irrational's sequence ("digits") never
>>>>>>> terminates (i.e. it is an INFINITELY long sequence).
>>>>>
>>>>> Ignored this part I see.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> You are utterly clueless on these things.
>>>
>>> Projection.
>>>
>>>> The square-root of 2 does not jump around on the number line.
>>>
>>> Yes it does, all irrational numbers do.
>>>
>>> /Flibble
>>>
>>
>> So, what other values does it jump to besides the actual value of
>> sqrt(2)?
>
> It jumps to the next slightly more accurate value as the approximation
> increases in accuracy.
>
> /Flibble
>

So, you are just claiming that APPROXIMATIONS aren't exact, that again
seems to be just a silly tautology.

Yes, approximations to a number aren't exact, but that doesn't say
anything about the number itself.

Approximations to the number 1/3 (as a decimal) aren't exact, are you
saying that 1/3 isn't an exact number?

On Sun, 5 Jun 2022 12:57:56 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 6/5/22 12:37 PM, Mr Flibble wrote:
> > On Sun, 5 Jun 2022 12:17:48 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 6/5/22 11:34 AM, Mr Flibble wrote:
> >>> On Sun, 5 Jun 2022 16:28:05 +0100
> >>> Andy Walker <anw@cuboid.co.uk> wrote:
> >>>
> >>>> On 05/06/2022 14:47, Mr Flibble wrote:
> >>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> >>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>> [...] Sort of like how the number Pi has an
> >>>>>> exact value, but you can never actually express it (because it
> >>>>>> takes an infinite number of digits).
> >>>>> PI does not have an exact value; no irrational number has an
> >>>>> exact value.
> >>>>
> >>>> Of course "pi" has an exact value; as do [eg] "sqrt(2)",
> >>>> "e", and all the other computable real [and complex] numbers.
> >>>> Whether that value can be expressed in finite terms in some
> >>>> particular representation is quite another matter. That in turn
> >>>> depends on the representation; standard decimals is merely one
> >>>> [common] choice. Note that in symbolic computer systems, those
> >>>> computable reals are typically written "pi" [or whatever], and
> >>>> the computer works with that exactly, so that [eg] "sin^2 (pi/3)
> >>>> == 3/4", not 0.7499...; and also that in decimal-type notations
> >>>> most rationals equally have no terminating expansion. Numbers
> >>>> such as "pi" and "sqrt(2)" are not defined as decimal expansions
> >>>> but via their properties [eg that "sqrt(2)" is the unique
> >>>> positive real whose square is 2, or equivalently that it is the
> >>>> ratio of the diagonal of a square to its side, and "pi" is the
> >>>> least positive real whose sine is zero]. Those properties are
> >>>> exact, and tell you all you ever need to know about those
> >>>> numbers.
> >>>>
> >>>> [I have removed my name from the "Subject:"; I don't
> >>>> know why anyone saw fit to attach it to this debate, such as it
> >>>> is, on the HP.]
> >>>
> >>> What has decimal (base 10) expansion got to do with anything? An
> >>> irrational number has a non-terminating sequence in ANY base. I
> >>> am sorry but you are simply mistaken: irrational numbers do NOT
> >>> have an exact value; this is obvious to anyone who understands
> >>> logic and uses a sane definition for infinity.
> >>>
> >>> /Flibble
> >>>
> >>
> >> How about in base pi? then it is the number 10
> >
> > how about base banana? then it is the number 10.
> >
> > PI, like banana, is just a symbol representing an irrational number
> > that has no exact value. To use it here is circular and therefor
> > erroneous.
> >
> >>
> >> Base pi is an interesting base for some problems.
> >>
> >> What is your definition of "an exact value"?
> >>
> >> Maybe the problem is you don't quite understand the meaning of that
> >> term.
> >
> > Of course I understand the fucking term. For the purposes of this
> > discussion an exact value is a real number (non-integer) that
> > terminates in a base that is not a multiple of itself.
> >
> > /Flibble
> >
>
> Where do you get that definition from?
>
> So 1/3 isn't an exact value?

1/3 is 0.1 in base 3 so does have an exact value.

Let me rephrase: for the purposes of this discussion an exact value is
a real number that either terminates in some base or has a repetend in
other (non-irrational) bases.

/Flibble

On Sun, 5 Jun 2022 12:01:32 -0500
olcott <NoOne@NoWhere.com> wrote:

> On 6/5/2022 11:56 AM, Mr Flibble wrote:
> > On Sun, 5 Jun 2022 12:50:13 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 6/5/22 12:28 PM, Mr Flibble wrote:
> >>> On Sun, 5 Jun 2022 12:22:45 -0400
> >>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>
> >>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
> >>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
> >>>>> Alan Mackenzie <acm@muc.de> wrote:
> >>>>>
> >>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> >>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
> >>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
> >>>>>>
> >>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
> >>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> >>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>>>>>> [...] Sort of like how the number Pi has an
> >>>>>>>>>> exact value, but you can never actually express it (because
> >>>>>>>>>> it takes an infinite number of digits).
> >>>>>>>>> PI does not have an exact value; no irrational number has an
> >>>>>>>>> exact value.
> >>>>>>
> >>>>>>>> Of course "pi" has an exact value; as do [eg]
> >>>>>>>> "sqrt(2)", "e", and all the other computable real [and
> >>>>>>>> complex] numbers. Whether that value can be expressed in
> >>>>>>>> finite terms in some particular representation is quite
> >>>>>>>> another matter. That in turn depends on the representation;
> >>>>>>>> standard decimals is merely one [common] choice. Note that
> >>>>>>>> in symbolic computer systems, those computable reals are
> >>>>>>>> typically written "pi" [or whatever], and the computer works
> >>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
> >>>>>>>> 0.7499...; and also that in decimal-type notations most
> >>>>>>>> rationals equally have no terminating expansion. Numbers
> >>>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal
> >>>>>>>> expansions but via their properties [eg that "sqrt(2)" is
> >>>>>>>> the unique positive real whose square is 2, or equivalently
> >>>>>>>> that it is the ratio of the diagonal of a square to its
> >>>>>>>> side, and "pi" is the least positive real whose sine is
> >>>>>>>> zero]. Those properties are exact, and tell you all you
> >>>>>>>> ever need to know about those numbers.
> >>>>>>
> >>>>>> [ .... ]
> >>>>>>
> >>>>>>> What has decimal (base 10) expansion got to do with anything?
> >>>>>>> An irrational number has a non-terminating sequence in ANY
> >>>>>>> base. I am sorry but you are simply mistaken: irrational
> >>>>>>> numbers do NOT have an exact value; this is obvious to anyone
> >>>>>>> who understands logic and uses a sane definition for infinity.
> >>>>>>
> >>>>>> That irrational numbers are exact values is clear to anybody
> >>>>>> with a degree in maths. Definitions of "infinity" (of which
> >>>>>> there are many) have nothing to do with this.
> >>>>>
> >>>>> You are wrong and fractally so so your degree in maths appears
> >>>>> to be worthless. An irrational number's sequence is
> >>>>> statistically random, has no fixed point on the number line
> >>>>> ergo has no exact representation. Any number with no exact
> >>>>> representation has, by definition, no exact value, only an
> >>>>> approximation. Infinity has everything to do with this as an
> >>>>> irrational's sequence ("digits") never terminates (i.e. it is
> >>>>> an INFINITELY long sequence).
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> Nope. Irrational numbers DO have exact points on the number line.
> >>>>
> >>>> And what does representation have to do with exact value?
> >>>>
> >>>> Also, irrational numbers sequence of digits are not necessarily
> >>>> statistically random, in some representations, they can be VERY
> >>>> predictible for some numbers.
> >>>>
> >>>> One simple construction to show exact position, draw a box with
> >>>> sides exactly 1.
> >>>>
> >>>> Draw a line though opposite corners and make one point the value
> >>>> 0.
> >>>>
> >>>> The other corner will be EXACTLY at the point sqrt(2), so that
> >>>> irrational number has an exact point on the number line.
> >>>>
> >>>> You just don't understand what an exact value means, likely
> >>>> because you can't understand things that are somewhat abstract.
> >>>
> >>> An irrational number does not have an exact point on the number
> >>> line as it will move about as you "zoom in", you can keep "zooming
> >>> in" forever (i.e. infinitely) and it will keep moving about
> >>> because the number never terminates.
> >>>
> >>> If I couldn't understand things that are somewhat abstract then I
> >>> wouldn't have a computer science degree (BSc Hons) and 30 years of
> >>> industry experience.
> >>>
> >>> /Flibble
> >>>
> >>
> >> Then why do you think irrational numbers don't have an exact
> >> location?
> >>
> >> I know people with degrees (even with honors) and industry
> >> experiance that still show that they don't really understand what
> >> they are talking about.
> >>
> >> The "width" of the point representing the location of an irrational
> >> number is just as much "0" as that of a rational number, so
> >> specifies just as exact of a location.
> >>
> >> The fact that we can't write it in a rational base with a finite
> >> number of digits doesn't actally mean anything.
> >
> > 3.1415xxxxxxxxx (a)
> > 3.14159xxxxxxxx (b)
> >
> > (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
> > value "moves about" as accuracy increases.
> >
> > /Flibble
> >
>
> You are confusing the representation of the number in decimal digits
> with the actual number itself.
No, you are. I am merely pointing out that the number changes up to a
factor of 1/base as you evaluate it at increasing accuracy.

/Flibble

On Sun, 5 Jun 2022 13:05:09 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 6/5/22 12:56 PM, Mr Flibble wrote:
> > On Sun, 5 Jun 2022 12:50:13 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 6/5/22 12:28 PM, Mr Flibble wrote:
> >>> On Sun, 5 Jun 2022 12:22:45 -0400
> >>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>
> >>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
> >>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
> >>>>> Alan Mackenzie <acm@muc.de> wrote:
> >>>>>
> >>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> >>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
> >>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
> >>>>>>
> >>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
> >>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> >>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>>>>>> [...] Sort of like how the number Pi has an
> >>>>>>>>>> exact value, but you can never actually express it (because
> >>>>>>>>>> it takes an infinite number of digits).
> >>>>>>>>> PI does not have an exact value; no irrational number has an
> >>>>>>>>> exact value.
> >>>>>>
> >>>>>>>> Of course "pi" has an exact value; as do [eg]
> >>>>>>>> "sqrt(2)", "e", and all the other computable real [and
> >>>>>>>> complex] numbers. Whether that value can be expressed in
> >>>>>>>> finite terms in some particular representation is quite
> >>>>>>>> another matter. That in turn depends on the representation;
> >>>>>>>> standard decimals is merely one [common] choice. Note that
> >>>>>>>> in symbolic computer systems, those computable reals are
> >>>>>>>> typically written "pi" [or whatever], and the computer works
> >>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
> >>>>>>>> 0.7499...; and also that in decimal-type notations most
> >>>>>>>> rationals equally have no terminating expansion. Numbers
> >>>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal
> >>>>>>>> expansions but via their properties [eg that "sqrt(2)" is
> >>>>>>>> the unique positive real whose square is 2, or equivalently
> >>>>>>>> that it is the ratio of the diagonal of a square to its
> >>>>>>>> side, and "pi" is the least positive real whose sine is
> >>>>>>>> zero]. Those properties are exact, and tell you all you
> >>>>>>>> ever need to know about those numbers.
> >>>>>>
> >>>>>> [ .... ]
> >>>>>>
> >>>>>>> What has decimal (base 10) expansion got to do with anything?
> >>>>>>> An irrational number has a non-terminating sequence in ANY
> >>>>>>> base. I am sorry but you are simply mistaken: irrational
> >>>>>>> numbers do NOT have an exact value; this is obvious to anyone
> >>>>>>> who understands logic and uses a sane definition for
> >>>>>>> infinity.
> >>>>>>
> >>>>>> That irrational numbers are exact values is clear to anybody
> >>>>>> with a degree in maths. Definitions of "infinity" (of which
> >>>>>> there are many) have nothing to do with this.
> >>>>>
> >>>>> You are wrong and fractally so so your degree in maths appears
> >>>>> to be worthless. An irrational number's sequence is
> >>>>> statistically random, has no fixed point on the number line
> >>>>> ergo has no exact representation. Any number with no exact
> >>>>> representation has, by definition, no exact value, only an
> >>>>> approximation. Infinity has everything to do with this as an
> >>>>> irrational's sequence ("digits") never terminates (i.e. it is
> >>>>> an INFINITELY long sequence).
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> Nope. Irrational numbers DO have exact points on the number line.
> >>>>
> >>>> And what does representation have to do with exact value?
> >>>>
> >>>> Also, irrational numbers sequence of digits are not necessarily
> >>>> statistically random, in some representations, they can be VERY
> >>>> predictible for some numbers.
> >>>>
> >>>> One simple construction to show exact position, draw a box with
> >>>> sides exactly 1.
> >>>>
> >>>> Draw a line though opposite corners and make one point the value
> >>>> 0.
> >>>>
> >>>> The other corner will be EXACTLY at the point sqrt(2), so that
> >>>> irrational number has an exact point on the number line.
> >>>>
> >>>> You just don't understand what an exact value means, likely
> >>>> because you can't understand things that are somewhat abstract.
> >>>
> >>> An irrational number does not have an exact point on the number
> >>> line as it will move about as you "zoom in", you can keep "zooming
> >>> in" forever (i.e. infinitely) and it will keep moving about
> >>> because the number never terminates.
> >>>
> >>> If I couldn't understand things that are somewhat abstract then I
> >>> wouldn't have a computer science degree (BSc Hons) and 30 years of
> >>> industry experience.
> >>>
> >>> /Flibble
> >>>
> >>
> >> Then why do you think irrational numbers don't have an exact
> >> location?
> >>
> >> I know people with degrees (even with honors) and industry
> >> experiance that still show that they don't really understand what
> >> they are talking about.
> >>
> >> The "width" of the point representing the location of an irrational
> >> number is just as much "0" as that of a rational number, so
> >> specifies just as exact of a location.
> >>
> >> The fact that we can't write it in a rational base with a finite
> >> number of digits doesn't actally mean anything.
> >
> > 3.1415xxxxxxxxx (a)
> > 3.14159xxxxxxxx (b)
> >
> > (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
> > value "moves about" as accuracy increases.
> >
> > /Flibble
> >
>
> But (a) and (b) aren't "pi"

No, they are approximations of pi. The value of the approximation
changes up to a factor of 1/base as you evaluate it at increasing
accuracy.

>
> All you are showing is that approximations to numbers get better as
> they get better, which is just a strange tautology.

Yes and therefor they jump about on the number line as accuracy
increases.

>
> The number PI, has only one precise value, the exact ratio of the
> circumference of a circle to its diameter on a flat plane (which will
> always be the same).

pi cannot have a precise value as it neither terminates nor has a
repetend in any base.

>
> The fact that it can't be expressed, isn't an issue on exactness, but
> of finite representation.

We can only ever have a finite representation.

>
> Note, that the set of numbers with finite representation is a
> countable set, so it isn't surprising that the uncountable infinity
> of the reals (that includes the irrationals) is not all finitely
> expressible.

Stating the obvious.

/Flibble

On Sun, 5 Jun 2022 13:07:19 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 6/5/22 12:58 PM, Mr Flibble wrote:
> > On Sun, 5 Jun 2022 12:54:22 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 6/5/22 12:42 PM, Mr Flibble wrote:
> >>> On Sun, 5 Jun 2022 11:41:05 -0500
> >>> olcott <NoOne@NoWhere.com> wrote:
> >>>
> >>>> On 6/5/2022 11:38 AM, Mr Flibble wrote:
> >>>>> On Sun, 5 Jun 2022 16:34:18 -0000 (UTC)
> >>>>> Alan Mackenzie <acm@muc.de> wrote:
> >>>>>
> >>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> >>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
> >>>>>>> Alan Mackenzie <acm@muc.de> wrote:
> >>>>>>
> >>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> >>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
> >>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
> >>>>>>
> >>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
> >>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> >>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>>>>>>>>>> [...] Sort of like how the number Pi has an
> >>>>>>>>>>>> exact value, but you can never actually express it
> >>>>>>>>>>>> (because it takes an infinite number of digits).
> >>>>>>>>>>> PI does not have an exact value; no irrational number has
> >>>>>>>>>>> an exact value.
> >>>>>>
> >>>>>>>>>> Of course "pi" has an exact value; as do [eg]
> >>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
> >>>>>>>>>> complex] numbers. Whether that value can be expressed in
> >>>>>>>>>> finite terms in some particular representation is quite
> >>>>>>>>>> another matter. That in turn depends on the
> >>>>>>>>>> representation; standard decimals is merely one [common]
> >>>>>>>>>> choice. Note that in symbolic computer systems, those
> >>>>>>>>>> computable reals are typically written "pi" [or whatever],
> >>>>>>>>>> and the computer works with that exactly, so that [eg]
> >>>>>>>>>> "sin^2 (pi/3) == 3/4", not 0.7499...; and also that in
> >>>>>>>>>> decimal-type notations most rationals equally have no
> >>>>>>>>>> terminating expansion. Numbers such as "pi" and "sqrt(2)"
> >>>>>>>>>> are not defined as decimal expansions but via their
> >>>>>>>>>> properties [eg that "sqrt(2)" is the unique positive real
> >>>>>>>>>> whose square is 2, or equivalently that it is the ratio of
> >>>>>>>>>> the diagonal of a square to its side, and "pi" is the
> >>>>>>>>>> least positive real whose sine is zero]. Those properties
> >>>>>>>>>> are exact, and tell you all you ever need to know about
> >>>>>>>>>> those numbers.
> >>>>>>
> >>>>>>>> [ .... ]
> >>>>>>
> >>>>>>>>> What has decimal (base 10) expansion got to do with
> >>>>>>>>> anything? An irrational number has a non-terminating
> >>>>>>>>> sequence in ANY base. I am sorry but you are simply
> >>>>>>>>> mistaken: irrational numbers do NOT have an exact value;
> >>>>>>>>> this is obvious to anyone who understands logic and uses a
> >>>>>>>>> sane definition for infinity.
> >>>>>>
> >>>>>>>> That irrational numbers are exact values is clear to anybody
> >>>>>>>> with a degree in maths. Definitions of "infinity" (of which
> >>>>>>>> there are many) have nothing to do with this.
> >>>>>>
> >>>>>>> You are wrong and fractally so so your degree in maths appears
> >>>>>>> to be worthless.
> >>>>>>
> >>>>>> No, I am right, along with the world's other mathematics
> >>>>>> graduates. You are stuck in the distant (100s of years) past,
> >>>>>> when mathematicians were still puzzling over what you're
> >>>>>> puzzling over. The fundamentals of maths have been worked out,
> >>>>>> and you are in the position of an alchemist faced with modern
> >>>>>> chemistry.
> >>>>>
> >>>>> Pure assertion with NOTHING to back it up.
> >>>>>
> >>>>>>
> >>>>>>> An irrational number's sequence is statistically random, has
> >>>>>>> no fixed point on the number line ergo has no exact
> >>>>>>> representation. Any number with no exact representation has,
> >>>>>>> by definition, no exact value, only an approximation.
> >>>>>>> Infinity has everything to do with this as an irrational's
> >>>>>>> sequence ("digits") never terminates (i.e. it is an
> >>>>>>> INFINITELY long sequence).
> >>>>>
> >>>>> Ignored this part I see.
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> You are utterly clueless on these things.
> >>>
> >>> Projection.
> >>>
> >>>> The square-root of 2 does not jump around on the number line.
> >>>
> >>> Yes it does, all irrational numbers do.
> >>>
> >>> /Flibble
> >>>
> >>
> >> So, what other values does it jump to besides the actual value of
> >> sqrt(2)?
> >
> > It jumps to the next slightly more accurate value as the
> > approximation increases in accuracy.
> >
> > /Flibble
> >
>
> So, you are just claiming that APPROXIMATIONS aren't exact, that
> again seems to be just a silly tautology.
>
> Yes, approximations to a number aren't exact, but that doesn't say
> anything about the number itself.
>
> Approximations to the number 1/3 (as a decimal) aren't exact, are you
> saying that 1/3 isn't an exact number?

1/3 is an exact number as it either terminates or has a repetend in
some base.

/Flibble

On Sun, 5 Jun 2022 18:22:17 +0100
Mr Flibble <flibble@reddwarf.jmc> wrote:

> On Sun, 5 Jun 2022 13:05:09 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
> > On 6/5/22 12:56 PM, Mr Flibble wrote:
> > > On Sun, 5 Jun 2022 12:50:13 -0400
> > > Richard Damon <Richard@Damon-Family.org> wrote:
> > >
> > >> On 6/5/22 12:28 PM, Mr Flibble wrote:
> > >>> On Sun, 5 Jun 2022 12:22:45 -0400
> > >>> Richard Damon <Richard@Damon-Family.org> wrote:
> > >>>
> > >>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
> > >>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
> > >>>>> Alan Mackenzie <acm@muc.de> wrote:
> > >>>>>
> > >>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> > >>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
> > >>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
> > >>>>>>
> > >>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
> > >>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> > >>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> > >>>>>>>>>> [...] Sort of like how the number Pi has an
> > >>>>>>>>>> exact value, but you can never actually express it
> > >>>>>>>>>> (because it takes an infinite number of digits).
> > >>>>>>>>> PI does not have an exact value; no irrational number has
> > >>>>>>>>> an exact value.
> > >>>>>>
> > >>>>>>>> Of course "pi" has an exact value; as do [eg]
> > >>>>>>>> "sqrt(2)", "e", and all the other computable real [and
> > >>>>>>>> complex] numbers. Whether that value can be expressed in
> > >>>>>>>> finite terms in some particular representation is quite
> > >>>>>>>> another matter. That in turn depends on the
> > >>>>>>>> representation; standard decimals is merely one [common]
> > >>>>>>>> choice. Note that in symbolic computer systems, those
> > >>>>>>>> computable reals are typically written "pi" [or whatever],
> > >>>>>>>> and the computer works with that exactly, so that [eg]
> > >>>>>>>> "sin^2 (pi/3) == 3/4", not 0.7499...; and also that in
> > >>>>>>>> decimal-type notations most rationals equally have no
> > >>>>>>>> terminating expansion. Numbers such as "pi" and "sqrt(2)"
> > >>>>>>>> are not defined as decimal expansions but via their
> > >>>>>>>> properties [eg that "sqrt(2)" is the unique positive real
> > >>>>>>>> whose square is 2, or equivalently that it is the ratio of
> > >>>>>>>> the diagonal of a square to its side, and "pi" is the
> > >>>>>>>> least positive real whose sine is zero]. Those properties
> > >>>>>>>> are exact, and tell you all you ever need to know about
> > >>>>>>>> those numbers.
> > >>>>>>
> > >>>>>> [ .... ]
> > >>>>>>
> > >>>>>>> What has decimal (base 10) expansion got to do with
> > >>>>>>> anything? An irrational number has a non-terminating
> > >>>>>>> sequence in ANY base. I am sorry but you are simply
> > >>>>>>> mistaken: irrational numbers do NOT have an exact value;
> > >>>>>>> this is obvious to anyone who understands logic and uses a
> > >>>>>>> sane definition for infinity.
> > >>>>>>
> > >>>>>> That irrational numbers are exact values is clear to anybody
> > >>>>>> with a degree in maths. Definitions of "infinity" (of which
> > >>>>>> there are many) have nothing to do with this.
> > >>>>>
> > >>>>> You are wrong and fractally so so your degree in maths appears
> > >>>>> to be worthless. An irrational number's sequence is
> > >>>>> statistically random, has no fixed point on the number line
> > >>>>> ergo has no exact representation. Any number with no exact
> > >>>>> representation has, by definition, no exact value, only an
> > >>>>> approximation. Infinity has everything to do with this as an
> > >>>>> irrational's sequence ("digits") never terminates (i.e. it is
> > >>>>> an INFINITELY long sequence).
> > >>>>>
> > >>>>> /Flibble
> > >>>>>
> > >>>>
> > >>>> Nope. Irrational numbers DO have exact points on the number
> > >>>> line.
> > >>>>
> > >>>> And what does representation have to do with exact value?
> > >>>>
> > >>>> Also, irrational numbers sequence of digits are not necessarily
> > >>>> statistically random, in some representations, they can be VERY
> > >>>> predictible for some numbers.
> > >>>>
> > >>>> One simple construction to show exact position, draw a box with
> > >>>> sides exactly 1.
> > >>>>
> > >>>> Draw a line though opposite corners and make one point the
> > >>>> value 0.
> > >>>>
> > >>>> The other corner will be EXACTLY at the point sqrt(2), so that
> > >>>> irrational number has an exact point on the number line.
> > >>>>
> > >>>> You just don't understand what an exact value means, likely
> > >>>> because you can't understand things that are somewhat
> > >>>> abstract.
> > >>>
> > >>> An irrational number does not have an exact point on the number
> > >>> line as it will move about as you "zoom in", you can keep
> > >>> "zooming in" forever (i.e. infinitely) and it will keep moving
> > >>> about because the number never terminates.
> > >>>
> > >>> If I couldn't understand things that are somewhat abstract then
> > >>> I wouldn't have a computer science degree (BSc Hons) and 30
> > >>> years of industry experience.
> > >>>
> > >>> /Flibble
> > >>>
> > >>
> > >> Then why do you think irrational numbers don't have an exact
> > >> location?
> > >>
> > >> I know people with degrees (even with honors) and industry
> > >> experiance that still show that they don't really understand what
> > >> they are talking about.
> > >>
> > >> The "width" of the point representing the location of an
> > >> irrational number is just as much "0" as that of a rational
> > >> number, so specifies just as exact of a location.
> > >>
> > >> The fact that we can't write it in a rational base with a finite
> > >> number of digits doesn't actally mean anything.
> > >
> > > 3.1415xxxxxxxxx (a)
> > > 3.14159xxxxxxxx (b)
> > >
> > > (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
> > > value "moves about" as accuracy increases.
> > >
> > > /Flibble
> > >
> >
> > But (a) and (b) aren't "pi"
>
> No, they are approximations of pi. The value of the approximation
> changes up to a factor of 1/base as you evaluate it at increasing
> accuracy.

I of course meant base^n not 1/base.

/Flibble

On Sun, 5 Jun 2022 18:19:47 +0100
Mr Flibble <flibble@reddwarf.jmc> wrote:

> On Sun, 5 Jun 2022 12:01:32 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
> > On 6/5/2022 11:56 AM, Mr Flibble wrote:
> > > On Sun, 5 Jun 2022 12:50:13 -0400
> > > Richard Damon <Richard@Damon-Family.org> wrote:
> > >
> > >> On 6/5/22 12:28 PM, Mr Flibble wrote:
> > >>> On Sun, 5 Jun 2022 12:22:45 -0400
> > >>> Richard Damon <Richard@Damon-Family.org> wrote:
> > >>>
> > >>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
> > >>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
> > >>>>> Alan Mackenzie <acm@muc.de> wrote:
> > >>>>>
> > >>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
> > >>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
> > >>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
> > >>>>>>
> > >>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
> > >>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
> > >>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
> > >>>>>>>>>> [...] Sort of like how the number Pi has an
> > >>>>>>>>>> exact value, but you can never actually express it
> > >>>>>>>>>> (because it takes an infinite number of digits).
> > >>>>>>>>> PI does not have an exact value; no irrational number has
> > >>>>>>>>> an exact value.
> > >>>>>>
> > >>>>>>>> Of course "pi" has an exact value; as do [eg]
> > >>>>>>>> "sqrt(2)", "e", and all the other computable real [and
> > >>>>>>>> complex] numbers. Whether that value can be expressed in
> > >>>>>>>> finite terms in some particular representation is quite
> > >>>>>>>> another matter. That in turn depends on the
> > >>>>>>>> representation; standard decimals is merely one [common]
> > >>>>>>>> choice. Note that in symbolic computer systems, those
> > >>>>>>>> computable reals are typically written "pi" [or whatever],
> > >>>>>>>> and the computer works with that exactly, so that [eg]
> > >>>>>>>> "sin^2 (pi/3) == 3/4", not 0.7499...; and also that in
> > >>>>>>>> decimal-type notations most rationals equally have no
> > >>>>>>>> terminating expansion. Numbers such as "pi" and "sqrt(2)"
> > >>>>>>>> are not defined as decimal expansions but via their
> > >>>>>>>> properties [eg that "sqrt(2)" is the unique positive real
> > >>>>>>>> whose square is 2, or equivalently that it is the ratio of
> > >>>>>>>> the diagonal of a square to its side, and "pi" is the
> > >>>>>>>> least positive real whose sine is zero]. Those properties
> > >>>>>>>> are exact, and tell you all you ever need to know about
> > >>>>>>>> those numbers.
> > >>>>>>
> > >>>>>> [ .... ]
> > >>>>>>
> > >>>>>>> What has decimal (base 10) expansion got to do with
> > >>>>>>> anything? An irrational number has a non-terminating
> > >>>>>>> sequence in ANY base. I am sorry but you are simply
> > >>>>>>> mistaken: irrational numbers do NOT have an exact value;
> > >>>>>>> this is obvious to anyone who understands logic and uses a
> > >>>>>>> sane definition for infinity.
> > >>>>>>
> > >>>>>> That irrational numbers are exact values is clear to anybody
> > >>>>>> with a degree in maths. Definitions of "infinity" (of which
> > >>>>>> there are many) have nothing to do with this.
> > >>>>>
> > >>>>> You are wrong and fractally so so your degree in maths appears
> > >>>>> to be worthless. An irrational number's sequence is
> > >>>>> statistically random, has no fixed point on the number line
> > >>>>> ergo has no exact representation. Any number with no exact
> > >>>>> representation has, by definition, no exact value, only an
> > >>>>> approximation. Infinity has everything to do with this as an
> > >>>>> irrational's sequence ("digits") never terminates (i.e. it is
> > >>>>> an INFINITELY long sequence).
> > >>>>>
> > >>>>> /Flibble
> > >>>>>
> > >>>>
> > >>>> Nope. Irrational numbers DO have exact points on the number
> > >>>> line.
> > >>>>
> > >>>> And what does representation have to do with exact value?
> > >>>>
> > >>>> Also, irrational numbers sequence of digits are not necessarily
> > >>>> statistically random, in some representations, they can be VERY
> > >>>> predictible for some numbers.
> > >>>>
> > >>>> One simple construction to show exact position, draw a box with
> > >>>> sides exactly 1.
> > >>>>
> > >>>> Draw a line though opposite corners and make one point the
> > >>>> value 0.
> > >>>>
> > >>>> The other corner will be EXACTLY at the point sqrt(2), so that
> > >>>> irrational number has an exact point on the number line.
> > >>>>
> > >>>> You just don't understand what an exact value means, likely
> > >>>> because you can't understand things that are somewhat
> > >>>> abstract.
> > >>>
> > >>> An irrational number does not have an exact point on the number
> > >>> line as it will move about as you "zoom in", you can keep
> > >>> "zooming in" forever (i.e. infinitely) and it will keep moving
> > >>> about because the number never terminates.
> > >>>
> > >>> If I couldn't understand things that are somewhat abstract then
> > >>> I wouldn't have a computer science degree (BSc Hons) and 30
> > >>> years of industry experience.
> > >>>
> > >>> /Flibble
> > >>>
> > >>
> > >> Then why do you think irrational numbers don't have an exact
> > >> location?
> > >>
> > >> I know people with degrees (even with honors) and industry
> > >> experiance that still show that they don't really understand what
> > >> they are talking about.
> > >>
> > >> The "width" of the point representing the location of an
> > >> irrational number is just as much "0" as that of a rational
> > >> number, so specifies just as exact of a location.
> > >>
> > >> The fact that we can't write it in a rational base with a finite
> > >> number of digits doesn't actally mean anything.
> > >
> > > 3.1415xxxxxxxxx (a)
> > > 3.14159xxxxxxxx (b)
> > >
> > > (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
> > > value "moves about" as accuracy increases.
> > >
> > > /Flibble
> > >
> >
> > You are confusing the representation of the number in decimal
> > digits with the actual number itself.
>
> No, you are. I am merely pointing out that the number changes up to a
> factor of 1/base as you evaluate it at increasing accuracy.

I of course meant base^n not 1/base.

/Flibble

On 05/06/2022 18:05, Richard Damon wrote:
> Note, that the set of numbers with finite representation is a
> countable set, so it isn't surprising that the uncountable infinity
> of the reals (that includes the irrationals) is not all finitely
> expressible.

Perhaps worth noting that "almost all" real numbers have no form
of expression ["are indescribable"], because sentences, whether in English
or in the form of a computer program or any similar form, are themselves
countable. Every computable number [those for which a computer program
exists], a subset of those with descriptions, has a finite representation
[eg as that computer program]; that includes irrationals such as "pi",
"sqrt(2)" and "e", and /every/ number of practical interest in physics,
applied mathematics and other similar sciences.

FWIW, Mr Flibble perpetrated his same nonsense quite recently.
Whether he is a troll or simply ill-educated in mathematics can safely
be left to the reader's imagination.

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Palmgren

On Sun, 5 Jun 2022 18:44:08 +0100
Andy Walker <anw@cuboid.co.uk> wrote:

> On 05/06/2022 18:05, Richard Damon wrote:
> > Note, that the set of numbers with finite representation is a
> > countable set, so it isn't surprising that the uncountable infinity
> > of the reals (that includes the irrationals) is not all finitely
> > expressible.
>
> Perhaps worth noting that "almost all" real numbers have no
> form of expression ["are indescribable"], because sentences, whether
> in English or in the form of a computer program or any similar form,
> are themselves countable. Every computable number [those for which a
> computer program exists], a subset of those with descriptions, has a
> finite representation [eg as that computer program]; that includes
> irrationals such as "pi", "sqrt(2)" and "e", and /every/ number of
> practical interest in physics, applied mathematics and other similar
> sciences.
>
> FWIW, Mr Flibble perpetrated his same nonsense quite recently.
> Whether he is a troll or simply ill-educated in mathematics can safely
> be left to the reader's imagination.
FWIW, your mathematics degree is worthless as you don't understand the
basics; your mind has been clouded by the manipulation of symbols at
the expense of logic. I wouldn't like to see your code.

/Flibble

Andy Walker <anw@cuboid.co.uk> writes:

> [I have removed my name from the "Subject:"; I don't know why
> anyone saw fit to attach it to this debate, such as it is, on the HP.]

It was PO. It's a ploy to goad people into talking to him.

--
Ben.

On 6/5/2022 12:19 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:01:32 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 6/5/2022 11:56 AM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:50:13 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 12:28 PM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 12:22:45 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>>>
>>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>>>> exact value.
>>>>>>>>
>>>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>>>> finite terms in some particular representation is quite
>>>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>>>> standard decimals is merely one [common] choice. Note that
>>>>>>>>>> in symbolic computer systems, those computable reals are
>>>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>>>> rationals equally have no terminating expansion. Numbers
>>>>>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal
>>>>>>>>>> expansions but via their properties [eg that "sqrt(2)" is
>>>>>>>>>> the unique positive real whose square is 2, or equivalently
>>>>>>>>>> that it is the ratio of the diagonal of a square to its
>>>>>>>>>> side, and "pi" is the least positive real whose sine is
>>>>>>>>>> zero]. Those properties are exact, and tell you all you
>>>>>>>>>> ever need to know about those numbers.
>>>>>>>>
>>>>>>>> [ .... ]
>>>>>>>>
>>>>>>>>> What has decimal (base 10) expansion got to do with anything?
>>>>>>>>> An irrational number has a non-terminating sequence in ANY
>>>>>>>>> base. I am sorry but you are simply mistaken: irrational
>>>>>>>>> numbers do NOT have an exact value; this is obvious to anyone
>>>>>>>>> who understands logic and uses a sane definition for infinity.
>>>>>>>>
>>>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>>>> there are many) have nothing to do with this.
>>>>>>>
>>>>>>> You are wrong and fractally so so your degree in maths appears
>>>>>>> to be worthless. An irrational number's sequence is
>>>>>>> statistically random, has no fixed point on the number line
>>>>>>> ergo has no exact representation. Any number with no exact
>>>>>>> representation has, by definition, no exact value, only an
>>>>>>> approximation. Infinity has everything to do with this as an
>>>>>>> irrational's sequence ("digits") never terminates (i.e. it is
>>>>>>> an INFINITELY long sequence).
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Nope. Irrational numbers DO have exact points on the number line.
>>>>>>
>>>>>> And what does representation have to do with exact value?
>>>>>>
>>>>>> Also, irrational numbers sequence of digits are not necessarily
>>>>>> statistically random, in some representations, they can be VERY
>>>>>> predictible for some numbers.
>>>>>>
>>>>>> One simple construction to show exact position, draw a box with
>>>>>> sides exactly 1.
>>>>>>
>>>>>> Draw a line though opposite corners and make one point the value
>>>>>> 0.
>>>>>>
>>>>>> The other corner will be EXACTLY at the point sqrt(2), so that
>>>>>> irrational number has an exact point on the number line.
>>>>>>
>>>>>> You just don't understand what an exact value means, likely
>>>>>> because you can't understand things that are somewhat abstract.
>>>>>
>>>>> An irrational number does not have an exact point on the number
>>>>> line as it will move about as you "zoom in", you can keep "zooming
>>>>> in" forever (i.e. infinitely) and it will keep moving about
>>>>> because the number never terminates.
>>>>>
>>>>> If I couldn't understand things that are somewhat abstract then I
>>>>> wouldn't have a computer science degree (BSc Hons) and 30 years of
>>>>> industry experience.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Then why do you think irrational numbers don't have an exact
>>>> location?
>>>>
>>>> I know people with degrees (even with honors) and industry
>>>> experiance that still show that they don't really understand what
>>>> they are talking about.
>>>>
>>>> The "width" of the point representing the location of an irrational
>>>> number is just as much "0" as that of a rational number, so
>>>> specifies just as exact of a location.
>>>>
>>>> The fact that we can't write it in a rational base with a finite
>>>> number of digits doesn't actally mean anything.
>>>
>>> 3.1415xxxxxxxxx (a)
>>> 3.14159xxxxxxxx (b)
>>>
>>> (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
>>> value "moves about" as accuracy increases.
>>>
>>> /Flibble
>>>
>>
>> You are confusing the representation of the number in decimal digits
>> with the actual number itself.
>
> No, you are. I am merely pointing out that the number changes up to a
> factor of 1/base as you evaluate it at increasing accuracy.
>
> /Flibble
>

Every real number has a unique point on the number line.
These points do not jump around.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 6/5/2022 12:56 PM, Ben wrote:
> Andy Walker <anw@cuboid.co.uk> writes:
>
>> [I have removed my name from the "Subject:"; I don't know why
>> anyone saw fit to attach it to this debate, such as it is, on the HP.]
>
> It was PO. It's a ploy to goad people into talking to him.
>

I was my specific reply to Andy Walker's incorrect reasoning.
It was claimed that others have considered simulating halt deciders
before. I proved otherwise.

The fact that no rebuttal has been made is construed as acknowledgement
that I am correct.

No one ever bothered to think the otherwise "impossible" input being
analyzed by a simulating halt decider ALL THE WAY THROUGH EVER BEFORE!

On 6/2/2022 1:12 PM, Andy Walker wrote:
> http://www.cuboid.me.uk/anw/G12FCO/lect18.html
At any given moment as the emulation proceeds, we are in one of not two
but three states: the program has halted, or it is looping, or it is
still running and has not yet entered a loop. It's the third case that
kills us -- we just have to keep going, and wait for one of the other
two things to happen. The trouble is that it may be that neither of them
ever happens -- which is why `it must be in a loop' was in quotes above.

Andy Walker did provide a fundamentally flawed and totally shallow
analysis of an simulating halt decider.

At any given moment as the emulation proceeds,
we are in one of not two but three states:
(a) The program has halted,
(b) It is still running.
(c) IT HAS MATCHED AN INFINITE BEHAVIOR PATTERN

void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
return;
}

The above matches (c) for infinitely nested simulation.

H(P,P)==0 does correctly map the otherwise impossible input to a reject
state.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Mr Flibble <flibble@reddwarf.jmc> wrote:
> On Sun, 5 Jun 2022 12:57:56 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:

[ .... ]

>> So 1/3 isn't an exact value?

> 1/3 is 0.1 in base 3 so does have an exact value.

> Let me rephrase: for the purposes of this discussion an exact value is
> a real number that either terminates in some base or has a repetend in
> other (non-irrational) bases.

So what you seem to be saying is that an exact value is a rational
number. That, somehow, irrational numbers are inexact. There is no
basis in modern maths for that last assertion. But for that rider - "for
the purposes of this discussion" shows that you wish to have a discussion
based on falsehood and superstition.

> /Flibble

--
Alan Mackenzie (Nuremberg, Germany).

On 6/5/22 1:19 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:01:32 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 6/5/2022 11:56 AM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:50:13 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 12:28 PM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 12:22:45 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>>>
>>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>>>> exact value.
>>>>>>>>
>>>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>>>> finite terms in some particular representation is quite
>>>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>>>> standard decimals is merely one [common] choice. Note that
>>>>>>>>>> in symbolic computer systems, those computable reals are
>>>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>>>> rationals equally have no terminating expansion. Numbers
>>>>>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal
>>>>>>>>>> expansions but via their properties [eg that "sqrt(2)" is
>>>>>>>>>> the unique positive real whose square is 2, or equivalently
>>>>>>>>>> that it is the ratio of the diagonal of a square to its
>>>>>>>>>> side, and "pi" is the least positive real whose sine is
>>>>>>>>>> zero]. Those properties are exact, and tell you all you
>>>>>>>>>> ever need to know about those numbers.
>>>>>>>>
>>>>>>>> [ .... ]
>>>>>>>>
>>>>>>>>> What has decimal (base 10) expansion got to do with anything?
>>>>>>>>> An irrational number has a non-terminating sequence in ANY
>>>>>>>>> base. I am sorry but you are simply mistaken: irrational
>>>>>>>>> numbers do NOT have an exact value; this is obvious to anyone
>>>>>>>>> who understands logic and uses a sane definition for infinity.
>>>>>>>>
>>>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>>>> there are many) have nothing to do with this.
>>>>>>>
>>>>>>> You are wrong and fractally so so your degree in maths appears
>>>>>>> to be worthless. An irrational number's sequence is
>>>>>>> statistically random, has no fixed point on the number line
>>>>>>> ergo has no exact representation. Any number with no exact
>>>>>>> representation has, by definition, no exact value, only an
>>>>>>> approximation. Infinity has everything to do with this as an
>>>>>>> irrational's sequence ("digits") never terminates (i.e. it is
>>>>>>> an INFINITELY long sequence).
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Nope. Irrational numbers DO have exact points on the number line.
>>>>>>
>>>>>> And what does representation have to do with exact value?
>>>>>>
>>>>>> Also, irrational numbers sequence of digits are not necessarily
>>>>>> statistically random, in some representations, they can be VERY
>>>>>> predictible for some numbers.
>>>>>>
>>>>>> One simple construction to show exact position, draw a box with
>>>>>> sides exactly 1.
>>>>>>
>>>>>> Draw a line though opposite corners and make one point the value
>>>>>> 0.
>>>>>>
>>>>>> The other corner will be EXACTLY at the point sqrt(2), so that
>>>>>> irrational number has an exact point on the number line.
>>>>>>
>>>>>> You just don't understand what an exact value means, likely
>>>>>> because you can't understand things that are somewhat abstract.
>>>>>
>>>>> An irrational number does not have an exact point on the number
>>>>> line as it will move about as you "zoom in", you can keep "zooming
>>>>> in" forever (i.e. infinitely) and it will keep moving about
>>>>> because the number never terminates.
>>>>>
>>>>> If I couldn't understand things that are somewhat abstract then I
>>>>> wouldn't have a computer science degree (BSc Hons) and 30 years of
>>>>> industry experience.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Then why do you think irrational numbers don't have an exact
>>>> location?
>>>>
>>>> I know people with degrees (even with honors) and industry
>>>> experiance that still show that they don't really understand what
>>>> they are talking about.
>>>>
>>>> The "width" of the point representing the location of an irrational
>>>> number is just as much "0" as that of a rational number, so
>>>> specifies just as exact of a location.
>>>>
>>>> The fact that we can't write it in a rational base with a finite
>>>> number of digits doesn't actally mean anything.
>>>
>>> 3.1415xxxxxxxxx (a)
>>> 3.14159xxxxxxxx (b)
>>>
>>> (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
>>> value "moves about" as accuracy increases.
>>>
>>> /Flibble
>>>
>>
>> You are confusing the representation of the number in decimal digits
>> with the actual number itself.
>
> No, you are. I am merely pointing out that the number changes up to a
> factor of 1/base as you evaluate it at increasing accuracy.
>
> /Flibble
>

But APPROXIMATIONS to the number are not the number itself.

The irrational number all have an EXACT location on the number line.

On 6/5/22 1:22 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 13:05:09 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:56 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:50:13 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 12:28 PM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 12:22:45 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 6/5/22 11:49 AM, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>>>
>>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>>>> exact value, but you can never actually express it (because
>>>>>>>>>>>> it takes an infinite number of digits).
>>>>>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>>>>>> exact value.
>>>>>>>>
>>>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>>>> finite terms in some particular representation is quite
>>>>>>>>>> another matter. That in turn depends on the representation;
>>>>>>>>>> standard decimals is merely one [common] choice. Note that
>>>>>>>>>> in symbolic computer systems, those computable reals are
>>>>>>>>>> typically written "pi" [or whatever], and the computer works
>>>>>>>>>> with that exactly, so that [eg] "sin^2 (pi/3) == 3/4", not
>>>>>>>>>> 0.7499...; and also that in decimal-type notations most
>>>>>>>>>> rationals equally have no terminating expansion. Numbers
>>>>>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal
>>>>>>>>>> expansions but via their properties [eg that "sqrt(2)" is
>>>>>>>>>> the unique positive real whose square is 2, or equivalently
>>>>>>>>>> that it is the ratio of the diagonal of a square to its
>>>>>>>>>> side, and "pi" is the least positive real whose sine is
>>>>>>>>>> zero]. Those properties are exact, and tell you all you
>>>>>>>>>> ever need to know about those numbers.
>>>>>>>>
>>>>>>>> [ .... ]
>>>>>>>>
>>>>>>>>> What has decimal (base 10) expansion got to do with anything?
>>>>>>>>> An irrational number has a non-terminating sequence in ANY
>>>>>>>>> base. I am sorry but you are simply mistaken: irrational
>>>>>>>>> numbers do NOT have an exact value; this is obvious to anyone
>>>>>>>>> who understands logic and uses a sane definition for
>>>>>>>>> infinity.
>>>>>>>>
>>>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>>>> there are many) have nothing to do with this.
>>>>>>>
>>>>>>> You are wrong and fractally so so your degree in maths appears
>>>>>>> to be worthless. An irrational number's sequence is
>>>>>>> statistically random, has no fixed point on the number line
>>>>>>> ergo has no exact representation. Any number with no exact
>>>>>>> representation has, by definition, no exact value, only an
>>>>>>> approximation. Infinity has everything to do with this as an
>>>>>>> irrational's sequence ("digits") never terminates (i.e. it is
>>>>>>> an INFINITELY long sequence).
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Nope. Irrational numbers DO have exact points on the number line.
>>>>>>
>>>>>> And what does representation have to do with exact value?
>>>>>>
>>>>>> Also, irrational numbers sequence of digits are not necessarily
>>>>>> statistically random, in some representations, they can be VERY
>>>>>> predictible for some numbers.
>>>>>>
>>>>>> One simple construction to show exact position, draw a box with
>>>>>> sides exactly 1.
>>>>>>
>>>>>> Draw a line though opposite corners and make one point the value
>>>>>> 0.
>>>>>>
>>>>>> The other corner will be EXACTLY at the point sqrt(2), so that
>>>>>> irrational number has an exact point on the number line.
>>>>>>
>>>>>> You just don't understand what an exact value means, likely
>>>>>> because you can't understand things that are somewhat abstract.
>>>>>
>>>>> An irrational number does not have an exact point on the number
>>>>> line as it will move about as you "zoom in", you can keep "zooming
>>>>> in" forever (i.e. infinitely) and it will keep moving about
>>>>> because the number never terminates.
>>>>>
>>>>> If I couldn't understand things that are somewhat abstract then I
>>>>> wouldn't have a computer science degree (BSc Hons) and 30 years of
>>>>> industry experience.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Then why do you think irrational numbers don't have an exact
>>>> location?
>>>>
>>>> I know people with degrees (even with honors) and industry
>>>> experiance that still show that they don't really understand what
>>>> they are talking about.
>>>>
>>>> The "width" of the point representing the location of an irrational
>>>> number is just as much "0" as that of a rational number, so
>>>> specifies just as exact of a location.
>>>>
>>>> The fact that we can't write it in a rational base with a finite
>>>> number of digits doesn't actally mean anything.
>>>
>>> 3.1415xxxxxxxxx (a)
>>> 3.14159xxxxxxxx (b)
>>>
>>> (b) is nearer to 3.14160 than 3.14150 that (a) indicates hence its
>>> value "moves about" as accuracy increases.
>>>
>>> /Flibble
>>>
>>
>> But (a) and (b) aren't "pi"
>
> No, they are approximations of pi. The value of the approximation
> changes up to a factor of 1/base as you evaluate it at increasing
> accuracy.
>
>>
>> All you are showing is that approximations to numbers get better as
>> they get better, which is just a strange tautology.
>
> Yes and therefor they jump about on the number line as accuracy
> increases.
>
>>
>> The number PI, has only one precise value, the exact ratio of the
>> circumference of a circle to its diameter on a flat plane (which will
>> always be the same).
>
> pi cannot have a precise value as it neither terminates nor has a
> repetend in any base.
>
>>
>> The fact that it can't be expressed, isn't an issue on exactness, but
>> of finite representation.
>
> We can only ever have a finite representation.
>
>>
>> Note, that the set of numbers with finite representation is a
>> countable set, so it isn't surprising that the uncountable infinity
>> of the reals (that includes the irrationals) is not all finitely
>> expressible.
>
> Stating the obvious.
>
> /Flibble
>

On 6/5/22 1:23 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 13:07:19 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:58 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:54:22 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 12:42 PM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 11:41:05 -0500
>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>
>>>>>> On 6/5/2022 11:38 AM, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 16:34:18 -0000 (UTC)
>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>>
>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>> On Sun, 5 Jun 2022 15:44:32 -0000 (UTC)
>>>>>>>>> Alan Mackenzie <acm@muc.de> wrote:
>>>>>>>>
>>>>>>>>>> Mr Flibble <flibble@reddwarf.jmc> wrote:
>>>>>>>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>>>>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>>>>
>>>>>>>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>>>>>>>> exact value, but you can never actually express it
>>>>>>>>>>>>>> (because it takes an infinite number of digits).
>>>>>>>>>>>>> PI does not have an exact value; no irrational number has
>>>>>>>>>>>>> an exact value.
>>>>>>>>
>>>>>>>>>>>> Of course "pi" has an exact value; as do [eg]
>>>>>>>>>>>> "sqrt(2)", "e", and all the other computable real [and
>>>>>>>>>>>> complex] numbers. Whether that value can be expressed in
>>>>>>>>>>>> finite terms in some particular representation is quite
>>>>>>>>>>>> another matter. That in turn depends on the
>>>>>>>>>>>> representation; standard decimals is merely one [common]
>>>>>>>>>>>> choice. Note that in symbolic computer systems, those
>>>>>>>>>>>> computable reals are typically written "pi" [or whatever],
>>>>>>>>>>>> and the computer works with that exactly, so that [eg]
>>>>>>>>>>>> "sin^2 (pi/3) == 3/4", not 0.7499...; and also that in
>>>>>>>>>>>> decimal-type notations most rationals equally have no
>>>>>>>>>>>> terminating expansion. Numbers such as "pi" and "sqrt(2)"
>>>>>>>>>>>> are not defined as decimal expansions but via their
>>>>>>>>>>>> properties [eg that "sqrt(2)" is the unique positive real
>>>>>>>>>>>> whose square is 2, or equivalently that it is the ratio of
>>>>>>>>>>>> the diagonal of a square to its side, and "pi" is the
>>>>>>>>>>>> least positive real whose sine is zero]. Those properties
>>>>>>>>>>>> are exact, and tell you all you ever need to know about
>>>>>>>>>>>> those numbers.
>>>>>>>>
>>>>>>>>>> [ .... ]
>>>>>>>>
>>>>>>>>>>> What has decimal (base 10) expansion got to do with
>>>>>>>>>>> anything? An irrational number has a non-terminating
>>>>>>>>>>> sequence in ANY base. I am sorry but you are simply
>>>>>>>>>>> mistaken: irrational numbers do NOT have an exact value;
>>>>>>>>>>> this is obvious to anyone who understands logic and uses a
>>>>>>>>>>> sane definition for infinity.
>>>>>>>>
>>>>>>>>>> That irrational numbers are exact values is clear to anybody
>>>>>>>>>> with a degree in maths. Definitions of "infinity" (of which
>>>>>>>>>> there are many) have nothing to do with this.
>>>>>>>>
>>>>>>>>> You are wrong and fractally so so your degree in maths appears
>>>>>>>>> to be worthless.
>>>>>>>>
>>>>>>>> No, I am right, along with the world's other mathematics
>>>>>>>> graduates. You are stuck in the distant (100s of years) past,
>>>>>>>> when mathematicians were still puzzling over what you're
>>>>>>>> puzzling over. The fundamentals of maths have been worked out,
>>>>>>>> and you are in the position of an alchemist faced with modern
>>>>>>>> chemistry.
>>>>>>>
>>>>>>> Pure assertion with NOTHING to back it up.
>>>>>>>
>>>>>>>>
>>>>>>>>> An irrational number's sequence is statistically random, has
>>>>>>>>> no fixed point on the number line ergo has no exact
>>>>>>>>> representation. Any number with no exact representation has,
>>>>>>>>> by definition, no exact value, only an approximation.
>>>>>>>>> Infinity has everything to do with this as an irrational's
>>>>>>>>> sequence ("digits") never terminates (i.e. it is an
>>>>>>>>> INFINITELY long sequence).
>>>>>>>
>>>>>>> Ignored this part I see.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> You are utterly clueless on these things.
>>>>>
>>>>> Projection.
>>>>>
>>>>>> The square-root of 2 does not jump around on the number line.
>>>>>
>>>>> Yes it does, all irrational numbers do.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> So, what other values does it jump to besides the actual value of
>>>> sqrt(2)?
>>>
>>> It jumps to the next slightly more accurate value as the
>>> approximation increases in accuracy.
>>>
>>> /Flibble
>>>
>>
>> So, you are just claiming that APPROXIMATIONS aren't exact, that
>> again seems to be just a silly tautology.
>>
>> Yes, approximations to a number aren't exact, but that doesn't say
>> anything about the number itself.
>>
>> Approximations to the number 1/3 (as a decimal) aren't exact, are you
>> saying that 1/3 isn't an exact number?
>
> 1/3 is an exact number as it either terminates or has a repetend in
> some base.
>
> /Flibble
>
But "repeating" wasn't factor. You were looking at sequnces of numbers
to N digits, the fact that for 1/3 the pattern is predictable doesn't
change the fact that the approximations are of different values.

On 6/5/22 1:17 PM, Mr Flibble wrote:
> On Sun, 5 Jun 2022 12:57:56 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 12:37 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 12:17:48 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 11:34 AM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 16:28:05 +0100
>>>>> Andy Walker <anw@cuboid.co.uk> wrote:
>>>>>
>>>>>> On 05/06/2022 14:47, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 07:58:42 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>> [...] Sort of like how the number Pi has an
>>>>>>>> exact value, but you can never actually express it (because it
>>>>>>>> takes an infinite number of digits).
>>>>>>> PI does not have an exact value; no irrational number has an
>>>>>>> exact value.
>>>>>>
>>>>>> Of course "pi" has an exact value; as do [eg] "sqrt(2)",
>>>>>> "e", and all the other computable real [and complex] numbers.
>>>>>> Whether that value can be expressed in finite terms in some
>>>>>> particular representation is quite another matter. That in turn
>>>>>> depends on the representation; standard decimals is merely one
>>>>>> [common] choice. Note that in symbolic computer systems, those
>>>>>> computable reals are typically written "pi" [or whatever], and
>>>>>> the computer works with that exactly, so that [eg] "sin^2 (pi/3)
>>>>>> == 3/4", not 0.7499...; and also that in decimal-type notations
>>>>>> most rationals equally have no terminating expansion. Numbers
>>>>>> such as "pi" and "sqrt(2)" are not defined as decimal expansions
>>>>>> but via their properties [eg that "sqrt(2)" is the unique
>>>>>> positive real whose square is 2, or equivalently that it is the
>>>>>> ratio of the diagonal of a square to its side, and "pi" is the
>>>>>> least positive real whose sine is zero]. Those properties are
>>>>>> exact, and tell you all you ever need to know about those
>>>>>> numbers.
>>>>>>
>>>>>> [I have removed my name from the "Subject:"; I don't
>>>>>> know why anyone saw fit to attach it to this debate, such as it
>>>>>> is, on the HP.]
>>>>>
>>>>> What has decimal (base 10) expansion got to do with anything? An
>>>>> irrational number has a non-terminating sequence in ANY base. I
>>>>> am sorry but you are simply mistaken: irrational numbers do NOT
>>>>> have an exact value; this is obvious to anyone who understands
>>>>> logic and uses a sane definition for infinity.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> How about in base pi? then it is the number 10
>>>
>>> how about base banana? then it is the number 10.
>>>
>>> PI, like banana, is just a symbol representing an irrational number
>>> that has no exact value. To use it here is circular and therefor
>>> erroneous.
>>>
>>>>
>>>> Base pi is an interesting base for some problems.
>>>>
>>>> What is your definition of "an exact value"?
>>>>
>>>> Maybe the problem is you don't quite understand the meaning of that
>>>> term.
>>>
>>> Of course I understand the fucking term. For the purposes of this
>>> discussion an exact value is a real number (non-integer) that
>>> terminates in a base that is not a multiple of itself.
>>>
>>> /Flibble
>>>
>>
>> Where do you get that definition from?
>>
>> So 1/3 isn't an exact value?
>
> 1/3 is 0.1 in base 3 so does have an exact value.

And base 3 is a multiple of 1/3, which you said wasn't allowed.

>
> Let me rephrase: for the purposes of this discussion an exact value is
> a real number that either terminates in some base or has a repetend in
> other (non-irrational) bases.
>
> /Flibble
>

No, that is NOT a correct definition. That isn't a bad definition of a
RATIONAL number, as any number that can be written as a finite string,
or a string with a repetend can be also expressed as a ratio of two numbers.

There is nothing in the actual meaning of "exact value" that needs the
value to be expressible as a finite string of digits.

On 6/5/22 2:07 PM, olcott wrote:
> On 6/5/2022 12:56 PM, Ben wrote:
>> Andy Walker <anw@cuboid.co.uk> writes:
>>
>>>     [I have removed my name from the "Subject:";  I don't know why
>>> anyone saw fit to attach it to this debate, such as it is, on the HP.]
>>
>> It was PO.  It's a ploy to goad people into talking to him.
>>
>
> I was my specific reply to Andy Walker's incorrect reasoning.
> It was claimed that others have considered simulating halt deciders
> before. I proved otherwise.
>
> The fact that no rebuttal has been made is construed as acknowledgement
> that I am correct.

The fact that rebuttals HAVE been made, proves you are a LIAR.

>
>
> No one ever bothered to think the otherwise "impossible" input being
> analyzed by a simulating halt decider ALL THE WAY THROUGH EVER BEFORE!

Except that you don't think your thought all the way through shows you
are an idiot.

>
> On 6/2/2022 1:12 PM, Andy Walker wrote:
> >  http://www.cuboid.me.uk/anw/G12FCO/lect18.html
> At any given moment as the emulation proceeds, we are in one of not two
> but three states: the program has halted, or it is looping, or it is
> still running and has not yet entered a loop. It's the third case that
> kills us -- we just have to keep going, and wait for one of the other
> two things to happen. The trouble is that it may be that neither of them
> ever happens -- which is why `it must be in a loop' was in quotes above.
>
> Andy Walker did provide a fundamentally flawed and totally shallow
> analysis of an simulating halt decider.
>
> At any given moment as the emulation proceeds,
> we are in one of not two but three states:
> (a) The program has halted,
> (b) It is still running.
> (c) IT HAS MATCHED AN INFINITE BEHAVIOR PATTERN
>
> void P(u32 x)
> {
>   if (H(x, x))
>     HERE: goto HERE;
>   return;
> }
>
> The above matches (c) for infinitely nested simulation.

Except it doesn't, the pattern at that point in NOT infinitely nested if
H(P,P) returns 0.

>
> H(P,P)==0 does correctly map the otherwise impossible input to a reject
> state.
>
>

Nope.

If H(P,P) == 0, then P(P) Halts, so it was in (b) when H aborted its
simulation and eventually makes it to (a).

H only THINKS it was (c) because H is using unsound and invalid logic.

On 6/5/22 1:02 PM, olcott wrote:
> On 6/5/2022 11:59 AM, Richard Damon wrote:
>> On 6/5/22 12:39 PM, olcott wrote:
>>> On 6/5/2022 11:31 AM, Richard Damon wrote:
>>>> On 6/5/22 11:57 AM, olcott wrote:
>>>>> On 6/5/2022 7:38 AM, Ben wrote:
>>>>>> Alan Mackenzie <acm@muc.de> writes:
>>>>>>
>>>>>>> olcott <NoOne@nowhere.com> wrote:
>>>>>>>> On 6/5/2022 6:12 AM, Alan Mackenzie wrote:
>>>>>>
>>>>>>>>> ...  What would be the turing machine equivalent of an
>>>>>>>>> "abnormal termination" in C?
>>>>>>>
>>>>>>>> An aborted simulation.
>>>>>>>
>>>>>>> There's no such thing on a turing machine.  It either runs and
>>>>>>> halts, or
>>>>>>> it runs forever.
>>>>>>>
>>>>>>> Your aborted simulation is just one final state of a turing machine,
>>>>>>> which has thus halted.
>>>>>>
>>>>>> A year ago I tried to get PO to accept a few basic facts about the
>>>>>> topic.  One of these was
>>>>>>
>>>>>> (B) Every computation that halts, for whatever reason, is a halting
>>>>>>      computation.
>>>>>>
>>>>>> After much ducking a diving, PO replied "OK".
>>>>>>
>>>>>
>>>>> Whatever I said years ago has been superseded by my current
>>>>> understanding:
>>>>>
>>>>> Computation that halts ... the Turing machine will halt whenever it
>>>>> enters a final state. (Linz:1990:234)
>>>>>
>>>>>
>>>>
>>>> And H^ applied to <H^> will Halt if H applied to <H^> <H^> rejects
>>>> its input as non-halting, thus showing that the H was wrong.
>>>
>>> You are a brain dead moron on this point.
>>>
>>>
>>
>> Why, for speaking Truth that you can't counter?
>
> The actual truth is beyond your intellectual capacity on this point.
>

I cam say the same about you, but MY logic is actually correct, and
veriviable by others.

YOU live in a world that is only your own and fails to match the rules
the rest of the world follows.

On 6/5/2022 1:31 PM, Richard Damon wrote:
> On 6/5/22 1:02 PM, olcott wrote:
>> On 6/5/2022 11:59 AM, Richard Damon wrote:
>>> On 6/5/22 12:39 PM, olcott wrote:
>>>> On 6/5/2022 11:31 AM, Richard Damon wrote:
>>>>> On 6/5/22 11:57 AM, olcott wrote:
>>>>>> On 6/5/2022 7:38 AM, Ben wrote:
>>>>>>> Alan Mackenzie <acm@muc.de> writes:
>>>>>>>
>>>>>>>> olcott <NoOne@nowhere.com> wrote:
>>>>>>>>> On 6/5/2022 6:12 AM, Alan Mackenzie wrote:
>>>>>>>
>>>>>>>>>> ...  What would be the turing machine equivalent of an
>>>>>>>>>> "abnormal termination" in C?
>>>>>>>>
>>>>>>>>> An aborted simulation.
>>>>>>>>
>>>>>>>> There's no such thing on a turing machine.  It either runs and
>>>>>>>> halts, or
>>>>>>>> it runs forever.
>>>>>>>>
>>>>>>>> Your aborted simulation is just one final state of a turing
>>>>>>>> machine,
>>>>>>>> which has thus halted.
>>>>>>>
>>>>>>> A year ago I tried to get PO to accept a few basic facts about the
>>>>>>> topic.  One of these was
>>>>>>>
>>>>>>> (B) Every computation that halts, for whatever reason, is a halting
>>>>>>>      computation.
>>>>>>>
>>>>>>> After much ducking a diving, PO replied "OK".
>>>>>>>
>>>>>>
>>>>>> Whatever I said years ago has been superseded by my current
>>>>>> understanding:
>>>>>>
>>>>>> Computation that halts ... the Turing machine will halt whenever
>>>>>> it enters a final state. (Linz:1990:234)
>>>>>>
>>>>>>
>>>>>
>>>>> And H^ applied to <H^> will Halt if H applied to <H^> <H^> rejects
>>>>> its input as non-halting, thus showing that the H was wrong.
>>>>
>>>> You are a brain dead moron on this point.
>>>>
>>>>
>>>
>>> Why, for speaking Truth that you can't counter?
>>
>> The actual truth is beyond your intellectual capacity on this point.
>>
>
> I cam say the same about you, but MY logic is actually correct, and
> veriviable by others.
Everyone that claims that the correctly simulated input to H(P,P)
reaches its final state is woefully incompetent even at basic software
engineering.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer