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| From | Mr Flibble <flibble@reddwarf.jmc> |
|---|---|
| Newsgroups | comp.theory |
| Subject | Re: Refuting the HP proofs (adapted for software engineers) |
| Message-ID | <20220606174712.000039f0@reddwarf.jmc> (permalink) |
| References | (21 earlier) <nL7nK.65115$ntj.27275@fx15.iad> <20220605205620.00006729@reddwarf.jmc> <K38nK.47082$X_i.4514@fx18.iad> <20220605212319.0000040a@reddwarf.jmc> <t7kuc4$b5l$1@dont-email.me> |
| Organization | Jupiter Mining Corp |
| Date | 2022-06-06 17:47 +0100 |
On Mon, 6 Jun 2022 16:10:28 +0300
Mikko <mikko.levanto@iki.fi> wrote:
> 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.
Nonsense.
/Flibble
Back to comp.theory | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread
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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