Re: Refuting the HP proofs (adapted for software engineers)

From	Alan Mackenzie <acm@muc.de>
Newsgroups	comp.theory
Subject	Re: Refuting the HP proofs (adapted for software engineers)
Date	2022-06-05 15:44 +0000
Organization	muc.de e.V.
Message-ID	<t7ij10$1qaq$2@news.muc.de> (permalink)
References	(7 earlier) <V4qdnY-VjKcsDAH_nZ2dnUU7_83NnZ2d@giganews.com> <TT0nK.107168$45E8.72348@fx47.iad> <20220605144720.0000277a@reddwarf.jmc> <t7ii25$1ohb$1@gioia.aioe.org> <20220605163408.00005e3f@reddwarf.jmc>

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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.

> /Flibble

-- 
Alan Mackenzie (Nuremberg, Germany).

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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