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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Newsgroups | comp.theory |
| Subject | Re: Refuting the HP proofs (adapted for software engineers) |
| Date | 2022-06-06 16:10 +0300 |
| Organization | - |
| Message-ID | <t7kuc4$b5l$1@dont-email.me> (permalink) |
| References | (21 earlier) <20220605203320.000053a1@reddwarf.jmc> <nL7nK.65115$ntj.27275@fx15.iad> <20220605205620.00006729@reddwarf.jmc> <K38nK.47082$X_i.4514@fx18.iad> <20220605212319.0000040a@reddwarf.jmc> |
On 2022-06-05 20:23:19 +0000, Mr Flibble said:
> On Sun, 5 Jun 2022 16:09:13 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 6/5/22 3:56 PM, Mr Flibble wrote:
>>> On Sun, 5 Jun 2022 15:47:30 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 6/5/22 3:33 PM, Mr Flibble wrote:
>>>>> On Sun, 5 Jun 2022 15:30:45 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 6/5/22 3:17 PM, Mr Flibble wrote:
>>>>>>> On Sun, 5 Jun 2022 14:17:29 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>
>>>>>>>> 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
>>>>>>>>>
>>>>>>>>
>>>>>>>> So you DO have problems with abstractions.
>>>>>>>>
>>>>>>>> The problem is, we don't actually need the finite numerical
>>>>>>>> representation of a number if we have the definition of what
>>>>>>>> the number is (which is another sort of abstract finite
>>>>>>>> representation).
>>>>>>>>
>>>>>>>> The "finite representation" of pi is the ratio of the
>>>>>>>> circumference to the diameter of a circle on a plane.
>>>>>>>
>>>>>>> No, instead if you use logic you must come to the conclusion
>>>>>>> that there is no ratio of the circumference to the diameter of a
>>>>>>> circle: rational numbers describe ratios, irrational numbers do
>>>>>>> not. QED.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Then you don't understand what is a ratio. Rational numbers are
>>>>>> the ratio of INTEGERS, not all ratios. Ratios define the relative
>>>>>> magnatude of one number to another, ANY number.
>>>>>>
>>>>>> Since it is clear you don't understand the meaning of the basic
>>>>>> terms, your OPINION about the weightier things becomes suspect.
>>>>>
>>>>> Prove that there is a ratio between the circumference and diameter
>>>>> of a circle. Hint: you can't.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Ratio of numbers A and B is defined as A / B (assuming B is not 0)
>>>>
>>>> The circumference of the circle is a length of the arc all the way
>>>> around the circle, so is a real number.
>>>>
>>>> The diameter of the circle is the length of the line from one side
>>>> of the circle to the other through the center, so is a real number.
>>>> Assuming the circle is not degenerate to a point, that number is
>>>> not zero.
>>>>
>>>> Thus we have two real numbers, the second not zero, so by closure,
>>>> the first divided by the second is a real number.
>>>>
>>>> Thus those numbers have a ratio.
>>>
>>> But at least one of those numbers must be irrational otherwise the
>>> ratio would be a rational number ergo at least one of those numbers
>>> is inexact ergo the resulting ratio between the circumference
>>> and diameter of a circle must also be inexact which as an irrational
>>> number it is. QED.
>>>
>>> /Flibble
>>>
>>
>> You are ASSUMING that irrational numbers are inexact, and that is a
>> false statement so you logic is unsound.
>>
>> Note, the square root of 2 can be proved exact by simple geometric
>> construction, thus disproving your claim that irrational numbers are
>> inexact.
>>
>
> Lets not change the subject and stick with pi shall we?
>
> (1) You have defined a ratio to be A/B.
> (2) You have defined a rational number to be the ratio
> between two integers.
> (3) You have defined pi as the ratio between circumference, C and
> diameter, D, of a circle
> (4) pi is defined to be an irrational number.
No, pi is not defined to be an irrational number. It is proven to be
irrational, i.e., it is proven that every rational number is either
less than or greater than pi.
> Given all of the above C, D, or both must be irrational for the
> resultant ratio, pi, to also be irrational.
If C and D are numbers. Not if they are just lengths. The question
"is the distance from P to Q rational" is meaningless unless one
postulates that distances are numbers.
Mikko
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Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-03 17:17 -0500
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-03 18:50 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-06-04 00:35 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-03 18:56 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-03 20:20 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-03 22:51 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-06-04 03:01 -0700
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-04 10:11 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 11:38 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] olcott <NoOne@NoWhere.com> - 2022-06-04 10:51 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 12:11 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] olcott <NoOne@NoWhere.com> - 2022-06-04 11:25 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 13:15 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] olcott <NoOne@NoWhere.com> - 2022-06-04 12:23 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 14:09 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] olcott <NoOne@NoWhere.com> - 2022-06-04 13:14 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 14:31 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] olcott <NoOne@NoWhere.com> - 2022-06-04 13:39 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ BRAIN DEAD MORON ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 14:49 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Alan Mackenzie <acm@muc.de> - 2022-06-04 18:17 +0000
Re: Refuting the HP proofs (adapted for software engineers)[ Alan Mackenzie ] olcott <NoOne@NoWhere.com> - 2022-06-04 13:37 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Alan Mackenzie ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 14:54 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Alan Mackenzie ] olcott <NoOne@NoWhere.com> - 2022-06-04 14:01 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Alan Mackenzie ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 15:57 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Alan Mackenzie ] Alan Mackenzie <acm@muc.de> - 2022-06-04 19:02 +0000
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-04 14:28 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 16:05 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] [OT] Jeff Barnett <jbb@notatt.com> - 2022-06-04 17:30 -0600
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mikko <mikko.levanto@iki.fi> - 2022-06-05 13:14 +0300
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 05:34 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Alan Mackenzie <acm@muc.de> - 2022-06-05 11:12 +0000
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 06:21 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 07:58 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 14:47 +0100
Re: Refuting the HP proofs (adapted for software engineers) Andy Walker <anw@cuboid.co.uk> - 2022-06-05 16:28 +0100
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 16:34 +0100
Re: Refuting the HP proofs (adapted for software engineers) Alan Mackenzie <acm@muc.de> - 2022-06-05 15:44 +0000
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 16:49 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:22 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:28 +0100
Re: Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-05 11:35 -0500
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:50 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:56 +0100
Re: Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-05 12:01 -0500
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:19 +0100
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:27 +0100
Re: Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-05 12:58 -0500
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:13 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:14 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 17:46 -0400
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 13:05 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:22 +0100
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:26 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:17 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:17 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:30 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:33 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:47 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:56 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 16:09 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 21:23 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 16:32 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mikko <mikko.levanto@iki.fi> - 2022-06-06 16:10 +0300
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-06 17:47 +0100
Re: Refuting the HP proofs (adapted for software engineers) Andy Walker <anw@cuboid.co.uk> - 2022-06-05 18:44 +0100
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:48 +0100
Re: Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-05 11:29 -0500
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:53 -0400
Re: Refuting the HP proofs (adapted for software engineers) Alan Mackenzie <acm@muc.de> - 2022-06-05 16:34 +0000
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:38 +0100
Re: Refuting the HP proofs (adapted for software engineers) olcott <NoOne@NoWhere.com> - 2022-06-05 11:41 -0500
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:42 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:54 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:58 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 13:07 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:23 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:20 -0400
Re: Refuting the HP proofs (adapted for software engineers) Alan Mackenzie <acm@muc.de> - 2022-06-05 17:04 +0000
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:17 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:37 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:57 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 18:17 +0100
Re: Refuting the HP proofs (adapted for software engineers) Alan Mackenzie <acm@muc.de> - 2022-06-05 18:07 +0000
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:19 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:32 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:34 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:49 -0400
Re: Refuting the HP proofs (adapted for software engineers) Alan Mackenzie <acm@muc.de> - 2022-06-05 19:42 +0000
Re: Refuting the HP proofs (adapted for software engineers) Mikko <mikko.levanto@iki.fi> - 2022-06-06 16:03 +0300
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:24 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:18 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:38 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 20:44 +0100
Re: Refuting the HP proofs (adapted for software engineers) Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:54 -0400
Re: Refuting the HP proofs (adapted for software engineers) Ben <ben.usenet@bsb.me.uk> - 2022-06-05 18:56 +0100
Re: Refuting the HP proofs (adapted for software engineers) [ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 13:07 -0500
Re: Refuting the HP proofs (adapted for software engineers) [ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:29 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Alan Mackenzie <acm@muc.de> - 2022-06-05 12:14 +0000
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Ben <ben.usenet@bsb.me.uk> - 2022-06-05 13:38 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Ben <ben.usenet@bsb.me.uk> - 2022-06-05 16:17 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 10:59 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:29 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 10:57 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:31 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 11:39 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:59 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 12:02 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:31 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 13:35 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 14:54 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 13:57 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 14:09 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:25 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 14:33 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 15:43 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 11:24 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-06-05 15:46 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Alan Mackenzie <acm@muc.de> - 2022-06-05 15:16 +0000
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 11:10 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-06-05 21:07 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 15:15 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 21:28 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 15:36 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 16:44 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 16:38 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 15:41 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 16:57 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Jeff Barnett <jbb@notatt.com> - 2022-06-05 15:59 -0600
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-06-06 00:59 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Jeff Barnett <jbb@notatt.com> - 2022-06-05 18:24 -0600
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Ben <ben.usenet@bsb.me.uk> - 2022-06-06 01:40 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Jeff Barnett <jbb@notatt.com> - 2022-06-05 18:44 -0600
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 20:03 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 21:59 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 21:14 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 22:44 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-06-06 02:58 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 21:11 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 22:20 -0400
Re: Refuting the HP proofs (adapted for software engineers[ brand new computer science ] olcott <NoOne@NoWhere.com> - 2022-06-05 21:37 -0500
Re: Refuting the HP proofs (adapted for software engineers[ brand new computer science ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 22:52 -0400
Re: Refuting the HP proofs (adapted for software engineers[ brand new computer science ] olcott <NoOne@NoWhere.com> - 2022-06-05 22:03 -0500
Re: Refuting the HP proofs (adapted for software engineers[ brand new computer science ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 23:26 -0400
Re: Refuting the HP proofs (adapted for software engineers[ Ordinary software engineering ] olcott <NoOne@NoWhere.com> - 2022-06-05 22:41 -0500
Re: Refuting the HP proofs (adapted for software engineers[ Ordinary software engineering ] Richard Damon <Richard@Damon-Family.org> - 2022-06-06 00:17 -0400
Re: Refuting the HP proofs (adapted for software engineers[ Ordinary software engineering ] olcott <NoOne@NoWhere.com> - 2022-06-06 10:28 -0500
Re: Refuting the HP proofs (adapted for software engineers[ Ordinary software engineering ] Richard Damon <Richard@Damon-Family.org> - 2022-06-06 21:04 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 22:15 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 21:22 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 22:38 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Mike Terry ] olcott <NoOne@NoWhere.com> - 2022-06-05 19:27 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Mike Terry ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 20:56 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ members of c/c++ ] olcott <NoOne@NoWhere.com> - 2022-06-07 20:04 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ members of c/c++ ] Richard Damon <Richard@Damon-Family.org> - 2022-06-07 22:45 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Mike Terry ] Mr Flibble <flibble@reddwarf.jmc> - 2022-06-06 17:49 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Mike Terry ] olcott <NoOne@NoWhere.com> - 2022-06-06 11:59 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 11:07 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Mr Flibble <flibble@reddwarf.jmc> - 2022-06-05 17:12 +0100
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-05 11:15 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:45 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-05 12:41 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 06:27 -0400
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] olcott <NoOne@NoWhere.com> - 2022-06-04 10:28 -0500
Re: Refuting the HP proofs (adapted for software engineers)[ Andy Walker ] Richard Damon <Richard@Damon-Family.org> - 2022-06-04 11:51 -0400
Re: Refuting the HP proofs (adapted for software engineers) Mr Flibble <flibble@reddwarf.jmc.corp> - 2022-06-04 00:36 +0100
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