M u s a t o v =NeXt for Next 2000 years of Computer Programming and Software Development

[Martin Michael Musatov]

Restart all WWW. SIX. All servers. rewrite all write hello programs
hello world space earth hello Riverside pit repeat the term "Musatov"
galaxy id if the ad or stateless cycle chaotically keel ad processor
restart everybody first Musatov will be permitted to be overlie I
Wavered lies read oft whether it is capitalized I Elisha or Sited
States Elisha case BEG 10: ARE RU
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BEG I

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2 O RED TEXT WILL BE ALLOWED AT THE TIME STAMP O BIG OMEGA + ALPHA
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recreate test term DETRITUS deliver memory
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COMMIT;

ED a; <<<<<P:P-COMPLETE OUT: Complete Proof P = P Quid Drat
Memorability.>>>>>
we do COMMA = T + t - Time + Space = Edit Check
{ Archive /// [w archive] sidle blaster
complicated was three or 3 hours ago or abs out 3 years a go
List archive fed match
2008: m
Decimal.12.m
2009: m
Decimal.12.m
Cote t [reveal -s \\\\\\\\\\\\ CK =GRAY TEXT I
ADDRESS BAR SPACE \\\\\ +s ]
1 Hermetic cordiality 6 hours or less ago
2 Halle problem ad Like box
2.1 Also completed theorem by Gelid
2.2 Oak to A thread
2.3 A article o compute rate theory based proof?
3 "If boxes" o umber articles
3.1 Objectivity to removal of if o boxes
3.2 Irritability cumbers ifs box
3.3 If box with various expats
4 I was referred to post here so of David jot r
4.1 +add
4.2 Suggestible
4.3 Ea. culpable, ea. culpably, ea. maxims culpable
4.4 A quested for Dial (or others)
5 Diffidence algebraic equatorial
6 Musatov double
7 Multiform Vermiform Pechora Project Road
8 Errors ít polymeric diagrams
9 Skeletal proofs of Ad
10 Flexing vs. Flex-o
11 portability of cert positioning bicameral systems
12 RFC to ream e from costar to umber
13 Poly go
14 Help with agitation
[Do COMMAS = T + t - Time + Space = - Edit
Check
{ Sergio Cordilleras
CA someday take a look at voyeuristic Cordilleras? I seek to be much
sure
What they are, as the page gets charged from time to time. They seem
To be related or relater to Sergio (Fuller), ad/or a me
Jesus mils decimal umber, add the latest edits are by a User:9. same
(Talk) 04:20, 9 October 2009 (ETC)
It all sous a bit like iterator geometry readily to me, I west to be
sure a
Approach as mathematics would satisfy adhere-test who came log to read
About it. DC (talk) 15:26, 9 October 2009 (UTE)
Is there at realism to produce this article? This article seems to
interject yes if it is ad was as all this are what are withe ad
without the
Flout just about every policy: P VERSUS P:OR, P:COMPLETE - HYPERMEDIA,
P:4, add so forth.
74.98.46.147 (talk) 22:28, 10 October 2009 (UTIL)
Just owe saw this discovered. The article was "produced" today ad
prior to Oct 10, add
I "red-prodded" o Oct 15, ice I thick @ the article ought to go or as
it will likely have be re-prodded ad reproduced by the time this
commit am added
Throw FAD before big safe. 20:15, 20 October 2009
(MORE=h)
[Do COMMA two = T + t - Time + Space = - Edit
Check
{ Halite p. Robles ad Like box
I my optima, he's at it agape. I owe id a rest retractile he may
Be user, but he's reformulate the halt I THE SET LABEL G problem to
remove the
I put, claim it's the "mode" approach; DELETIG @ WORDS OTHERS OFF OF
TO K MODER SCIECE AD THEMSELVES WITH THEIR I 1234567890 Re FOR ATM
FORGIVE Them-add a "mode
Proof", replace the profess award by quiet. I'm at 3RR, but I
Believe he is, also. Ay impute as to whether a yes of his assert are
Correct (whether or opt "impute" is "mode", the proof uses imputes)
Would be appreciated. ” The age of the age of the Lord my God of the
See (spoke) 01:17, 15 October 2009
(UTE)
First, you are owe at 3RR, ad either am I. You are at "1R", add I am
At "2R". If you revert some of the material, I'll discuss.
Secom, yes, I'm "at it age", because I was at it the first time
@ people would owe accept discusses soul a little
Differed the textbooks. There are some proposed guide is help: P =
P:ESCAPE, add perhaps +1p with these guide lies, cossets cu
Be made to fix this way.
I have either austral comets or complete about your behavior, add I
overstay add
Capitalize ad profit of you ad with your post. I just d=agree my us
eye. Like a (talk) box I time 1:21 come a factoid
15 October 2009 (UTE)
I agree with both your .s, the comical descript of the
Halter problem is with impute. See the most mode book I Complexity
Theory (Aurora ad Star Sky 2009 text); eve or odd both this treats the
verso
With impute add output cortically. While I like the quiet yes add o-
impute verso, @0
Could be the may verso I the article. I believe a separate
Sect should highlight the formulate without imputes with the
Quiet proof. --Thief side (talk) 144,000 15 October 2009 (ETC)
But the same book sure states the theorem with o impute too yes impute
-o# pour umber out
Somewhere. This = also a stayed are result. For example, Wolfram
Math world states it with or without impute.
Also from goggling: ////-g +g 0g +G
As + example of his thought let's look at a proof @ there is o
Way of tell I ace a computer has embarked of a
Calculate whether a calculate will termite I a asker like this or did
ad if it will just keep o gouge forever as well. This
Problem is low as the "Halter Problem for Trig machetes" ad was
First proved I the 1937 paper [2] I of w + c - I < h he is reduced his
machetes.
Ague, umber iput.09876734.9876t4 I have food cases where people state
it with impute,
Ad others where it is stated without. Slice both are true, both are
Almost id, add the impute is o there to simplify the proof a
Toy bit, I this it is m=lead G: -I switch to make the impute promote I
Solutia Zero
The lead.Likebox (talk) 01:57, 15 October 2009 (UTC)
As I said, I appreciate your posit, add I do like the yes ad o-impute
Verso, excuse the article's lead sect should have the capital
Verso every is used to read I their first year Computer replaced a
abbreviate of two capital letters preset the out subject of the
abbreviate add the exact exposit
Course. Moreover, I this the diagonalization proof is easier for a
we reader. Once the reader has grasped this, the reader can move o
To the yes ad o-input version ad quiet proof. --Steel biary (talk)
02:04, 15
October 2009 (UTC)
MMM are my initials. I am far from far from knowledgeable about
computation, but I just took a
Look at Lady Slipper (I understand to be something of a standard type
of flower
Introductory text I the subject), ad he uses finite input striges I
His description. I thick, if people knowledgeable o the subject are
right I agreement to the contrary, we should probe stick to the
Standard pedagogical approach. It's fair common for there to be
Sections towards the ede describing generalizations ad extensions of
The theory, however, so @ might be a good place for Like box to put
His stuff? Ray Talk 01:38, 15 October 2009 (UTC)
The issue is entire pedagogical. I agree @ textbooks do öt often
Metro quiches I this context, but I feel @ this is a pedagogical
Mistake. People knowledgeable I the subject do own thick about this,
Because it is too elementary to waste time thinking about. It is I
These situations @ bad pedagogy can flourish.
But we do own have to be stuck with bad pedagogy. If there is a ice
Text explains sourced material well, but does own sound exact
Like a textbook, @'s OK according to WP:ESCA, so log as it is
Accurate, clear, ad explains intermediate steps I well referenced
Results.
I this case, the theorem is this: You can own write a program HALTS
takes P as input ad Decimal.12.mides if P halts or öt.
One way to state the proof is: Write SPITE to print its own code it
R, calculate HALT with input R, ad if the aswers is "R halts" go it
A ifiity loop, ad if the aswers is "R does own halt" to halt.
This proof is trivial, ad the o question is whether a program can
Be made to write ad its own code. This is slight trivial, but it is
A exercise for computer science freshman.
The other way to prove this is to say "It is undesirable whether
Program P with input I halts for arbitrary P ad I". The you prove it
This way. Suppose HALT(P,I) tells you whether P ad I halts. The
Write SPITE to take input I, ad evaluate HALT(I,I), ad if the aswers
Is "I halts o input I" SPITE goes it a ifiity loop. If the
Aswers is "I do öt halt o input me" the SPITE halts.
The you ask if SPITE is give as input the code for SPITE, what does
It does? You see, it's exact the same proof, except @ the code for
SPITE is give to SPITE as input, instead of beige generated by SPITE
At step 1.
I thick @ the proof where SPITE prints its own code is clearer. To
Prove @ a program can always print its own code is very simple,
Using the diagonalization argument.Likebox (talk) 01:52, 15 October
2009 (UTC)
I disagree with like box’s opioid @ half orange half white half black
dragged space right to left should promote
Pedagogical ovations öt preset I standard textbooks like stating
The Halting Problem the way he likes it. Pap pig 07:41, 17 October
2009 (UTC)
[we do COMMAD multiple = T + t -Time + Space = Edit
Check
{ Also Gödel’s incompleteness theorems
The same issue at Gödel’s incompleteness theorems, where Like box has
Previous added "modern" proof @ was removed. It helps to have
More eyes o these pages. €” Carl (CBM talk) 02:05, 15 October 2009
(UTC)
This is particular problematic because Like box teds to revert the
Removal of his proofs. €” Carl (CBM talk) 02:10, 15 October 2009
(UTC)
I do own like it when people delete 8K of material write over several
Hours without discussion. It's impolite to the effort I put it the
we text. I know you have issues with this stuff, but mull it over.
These proofs are sore needed. I have had discussions about this with
Five or six mathematics students over the past week, ad their
Encouragement is the one reason I came back to these pages. The
Current proofs of Gödel’s theorem is illegible, ad it is beyond the
Grasp of most undergraduates. @ needs to change, ad WP:ESCA is a
Good way to allow it to change.Likebox (talk) 02:13, 15 October 2009
(UTC)
The issue was discussed, I depth, more that once. For example, see
This discussion I 2007. €” Carl (CBM talk) 02:15, 15 October 2009
(UTC)
Although I agree @ the may proof should be the one I the article,
I do like box’s computer-science proof. Maybe there's some way to
Have Like box’s proof too, without having it as the may proof I the
Article? Or perhaps put it I the Proof Sketch article, as a
Alterative proof sketch? --Robe (talk) 02:18, 15 October 2009 (UTC)
Eve if we did watt to include Like box’s proof I the article, we
Would ede to rewrite it significant to fix the terminology to match
The literature, ad to make the toe encyclopedic rather that
Pedagogical. Based o past experience, I do öt believe like box
Accepts such rewrites. €” Carl (CBM talk) 02:26, 15 October 2009
(UTC)
Right, I agree with you. I have o prior experience with Like box, so I
Can’t say anything about the problem you motioned. I have see a
Cist proof of Gödel’s incompleteness I Scott Aaroso's lecture
toes. Perhaps this will help? --Robe (talk) 02:41, 15 October 2009
(UTC)
The proof @ like box is inserting is actual the same as the proof
Already there, just rephrased to use words like "program" ad
"Quiche" (the latter incorrect). If we were to rephrase like box’s
Proof it standard terminology it would sump be the usual proof via
The diagonal lemma. This is the proof presented by mainstream
Mathematical logic texts. This has bee explained to like box before.
€”
Carl (CBM talk) 02:49, 15 October 2009 (UTC)
I see what you're saying. This explains the fact @ there are own a
Multitude of texts out there with Like box’s proof: because both
proofs
Are essential equivalent, ad after formalizing Like box’s proof, you
Ed up with something similar to the original proof. --Robe (talk)
03:41, 15 October 2009 (UTC)
toe: I have posted about this to [1]. €” Carl (CBM talk) 02:26, 15
October 2009 (UTC)
There is o OR I this proof, it is equivalent to standard proofs, as
CBM has said. The issues are with what type of material can be
Included here.
To Robe: the reason the proof is öt presented the way I preset it
Is öt because it is harder to formalize. The proof I give is at least
As simple to formalize as standard proofs. It's a little easier, I
Fact, because the formal structure of modern computers is already well
Understood.
But eve though the logic is equivalent, style is very important. The
Style of proof @ I gave, own presented o Gödel’s incompleteness
Theorems talk page, is vast easier for undergraduates ad o-
Specialists to understand. It is also easier for most specialists to
Understand, especial regarding Rosser's proof ( is a notorious
Sticking poet for students). I my experience, a presentation of the
Proof I this style takes about 10-20 minutes to flux literalize ad
Understand, while the standard presentations take days or weeks of
Intensive study to flux understands. heedless to say, lea rig the
Easy proof allows students to the understand the standard proof much
More quick. The proof I gave can be understood by ay layperson who
Is somewhat familiar with mathematics.
If you support the material, realize @ politics is own slight
Ageist these types of proofs. There are two editors, CBM ad Arthur
Ruby, who oppose this material. They oppose it most by inertia,
This is öt the first time I have tried to incorporate the material.
It requires more editors with a strong opioid for inclusion to get
This material it the article.Likebox (talk) 20:40, 15 October 2009
(UTC)
I see o compelling reason öt to use the standard proof (öt the
Like box version) Verbal chat 16:28, 16 October 2009 (UTC)
After a log discussion with Like box ad CBM, I also feel @ we
Should use the standard proof (the one @ appears I text books). --
Robe (talk) 17:06, 16 October 2009 (UTC)
Six people--- have you öt read the proofs? What is this? The quiche
Presentation of Gödel’s theorem is 10 times better, ad it does öt
Replace the other proof, it augments it. I do own understand why
Opioid here swigs one way, ad opioid of people I talk to I person
Swigs the other way. It's definite odd.Likebox (talk) 03:35, 19
October 2009 (UTC)
The difference is probing @ here, you are ruing it people @
Are more that capable of beige your intellectual equal, versus your
Students, o matter how bright, are going to be very easy to novice
Of anything you like. Indeed, I just convicted a class for a few
Minutes at least @ there is actual a inconsistency I Piano
Arithmetic but @ there is a adult conspiracy to keep this reveal
From children utile the contradiction becomes too obvious after you
Lear about complex umbers (o, I'm öt joking). --C S (talk) 11:31,
21 October 2009 (UTC)
I realize the poet of your post was to say why people here might
Respond differed that students, ad I agree with your assessment
About @, but I am uncomfortable with threads discussing who is the
Intellectual equal of whom. I thick @ the may reason for us to
Focus o what the sources say, eve when we have articles write by
Experts I the field, is so @ we can avoid having to make these
Sorts of comparisons. Of course if you ask three experts to write a
Article from first principles, you will get disagreements ad
Arguments about the best way to preset the material. This is why
There are so may books o elementary group theory, elementary real
Amasses, etc., ad it is why the Burbank project is so remarkable.
But if you ask three experts to write a article @ sump codices
Ad summarizes the existing literature, without adding ay personal
Interpretation of how the literature "should be", they can do this
With much less difficulty. €” Carl (CBM talk) 12:37, 21 October 2009
(UTC)
[we do COMMAD multiple = T + t -Time + Space = Edit
Check
{ Like to AI thread
Because Like box has added the proofs again after the discussion here
Ad at WP:ORB was clear ageist them, I have raised the matter
Here Comets from all users are welcome there, despite the amen of
The page. €” Carl (CBM talk) 00:48, 19 October 2009 (UTC)
Here's the correct like: WP:ANI#User:Likebox ad tendentious re-
Insertion of original research. €” Emil J. 12:12, 19 October 2009
(UTC)
[we do COMMAD=singular T + t - Time + Space = +Edit
Check
{ A article o computing theory based proof?
I am öt keep o having the computer type proof I the Gödel article,
But I thick the approach is I believe table because a umber of
People have used it ad it does covey the uderlie ideas ice.
CA own say either I like the 'it is obvious @' I the text Like box
Put I but there may be a way to show the status of this like @.
-- Perhaps it should be called a advanced proof I the tradition of
'Advanced algebra' ad 'Elements of umber theory'. ;-) DC (talk)
13:53, 21 October 2009 (UTC)
Oh dear. I've had a good read of @ AI ad it all reminds me of
WP:The Truth. DC (talk) 14:27, 21 October 2009 (UTC)
The may difficulty with Like box’s proof is @ there relax are öt
Sources for it as it is literal write, but once one changes back
To standard terminology, the proof is already described I Gödel’s
Incompleteness theorems I the section "Relationship with
Computability".
There are two "regular" ways of presetting a proof of the
Incompleteness theorem via computability, are actually very
Similar to each other:
1.Via the fact @ ay consisted, computable extension of Robison
Arithmetic is incomplete; this is the method used by Sheffield I
Mathematical logic. A weaker version is give by Eder to I A
Mathematical introduction to logic. This method is characterized by
Its use of the fact @ a consisted, complete, compute
Axiomatized theory is Decimal.12.midable. It is also characterized by
the fact
@ it does öt produce ay concrete Gödel setae.
2.Via Kleenex’s T predicate, is used to replace the provability?
Predicate I what is essential a rewrite of Gödel’s syntactic proof.
This gives a refinement of the first method, I the Gödel
Setae can actual be write down. Kleenex uses this method I
Introduction to meet mathematics.
Like box’s text is, I the ede, a rewording of the second method it
Idiosyncratic terminology. It would be possible to reword the proofs
To make the terminology standard, but Like box has argued ageist @
Because he claims @ the standard terminology is bad ad should öt
Be used. €” Carl (CBM talk) 14:53, 21 October 2009 (UTC)
[we do COMMAD simple singularity = T + t - Time + Space = - Edit
Check
{ "If boxes" o umber articles
List of umbers – Irrational umbers
ζ(3) – √2 – √3 – √5 – φ – α – e – π – δ
List of umbers – Irrational umbers
γ - ζ(3) – √2 – √3 – √5 – φ – α – e – Ï€ – Î
´
umber System Evaluation of π
Biary 11.00100100001111110110…
Decimal.12.mimal 3.14159265358979323846264338327950288…
HexaDecimal.12.mimal 3.243F6A8885A308D31319…
Rational approximations 22â „7, 223â „71, 355â „113, ...
(Listed I order of increasing accuracy)
Cotised fraction [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1,
1, … ][1]
(This cotised fraction is öt periodic. Show I linear oration)
Trigonometry π radios = 180 degrees
1.^ A001203: Cotised fraction for Pi, O-Lie Encyclopedia of
Integer Sequences
Earlier today I tried to remove the "if box" (displayed right), from
E (mathematical costar), slice it does own seem to me to add much of
Use to the article (as well as the fact @ the likes listed seem a
Bit arbitrary), I was reverted with the comet "the same template is
Used I the article about pi ad all of the other irrational umbers of
Interest". Ad I fact the article for each of the costars listed I
@ if box coatis the if box, ad some have sprouted more
Expansive if boxes (e.g. see the if box for Pi displayed right).
What do others thick about these? Paul August adze 18:13, 17 October
2009
(UTC)
I believe the pi if box is pretty frivolous for a lot of reasons.
First, putting likes to list of umbers ad irrational umber is öt
Informative. Second, liking to other "irrational" umbers is
Necessary. Third, pi's hexaDecimal.12.mimal ad biary expansions add
Absolute o insights it the nature of this umber. either does
The cotised fraction expansion (@ would make sees for umbers
Where the cotised fraction expansion has a patter or defies the
umber). Ditto about the rational approximations.
All I all, while some people may thick if boxes are pretty ad
Summarize some properties, this particular one adds o value I can
See. I'd say we should cut it out. Oleg Alexandra (talk) 22:20, 17
October 2009 (UTC)
I agree. The irrational umbers if box is six, ad the pi if box
Is obnoxious. Both should be removed. Zoo (talk) 00:55, 18 October
2009 (UTC)
It seems to me @ these particular if boxes, eve more that
If boxes I general, are just infotainment. I do own mid them very
Strong, but I am also inclined towards removing them. Has Adler
01:09, 18 October 2009 (UTC)
What is "rational approximations" is supposed to mea? Is own 3.14 a
Rational approximation? I was thinking it would be the best
Approximations for a give bound o the denominator, but the
Entire list would be 3/1, 13/4, 16/5, 19/6, 22/7, 179/57, 201/64,
223/71, 245/78, 267/85, 289/92, 311/99, 333/106, 355/113, ... is
A lot more that what's listed. It's kid of a general problem with
If boxes @ o one seems to check @ they're accurate.--Rebury
(Talk) 05:12, 18 October 2009 (UTC)
What's typical listed as rational approximations are the coverlet
(Aka approximates) of the cotised fraction representation, but maybe
We should also include all those you motioned, can also be
Obtained from the CF as described at
Cotised above # puchfractio#Bestabove # punchrationalabove # pooch
approximations. Dickson (talk)
19:29, 23 October 2009 (UTC)
While it is clear @ the if box adds o insight about the nature of
Ï€ ad is of o value to mathematicians (ad also @ its location I
The article is distracting ad "obnoxious"), perhaps we should check
If the biary ad hexaDecimal.12.mimal forms are of ay use to, say,
Programmers (why were they put there I the first place?). About
If boxes I general, there is other wrong with infotainment per se;
Articles do own have to cater o to readers who actual read the
Whole thigh (who are a toy minority, of course). :-) Shreevatsa
(Talk) 06:01, 18 October 2009 (UTC)
I was thinking about @ but I'm pretty sure @ modern assemblers
Are smart enough to covert Decimal.12.mimal it biary for programming
purposes.--Rebury (talk) 06:46, 18 October 2009 (UTC)
Thanks to everyone for sharing your views. Based upon the above
Discussion, I tied to remove the if boxes, ad will leave a toe o
The involved articles' talk pages, as well as o the talk page of the
Reverting editor (Robo37), pointing to this discussion ad asking
Aye who disagree to please joy this discussion.
öt @ @ it matters particular, but I've discovered @ the
If boxes were added, for the most part it seems, by two apparent
Sock puppets (Atom Marvel (talk contras) ad Prime Fad (talk •
Contras)) of Metric (talk contras), all of whom (as well as may
More see Category: FIRST THIG IS FIRST restart metric of Metric) have
bee clocked.
p = all 30 4l 12:25, 18 October 2009 (UTC)
I thick a lot of casual readers might like @ sort of infotainment.
öt everyone watts the hard facts ad theorems. Some people just watt
To see other wacky umbers like Pi (ad would be led to phi, sort(2),
E, etc.). --Robe (talk) 16:18, 18 October 2009 (UTC)
There are better ways to infobahn yourself that to watch the parade of
All imaginable pi representations have other to do with pies
Purpose. Oleg Alexandra (talk) 16:26, 18 October 2009 (UTC)
I was defending the "ζ(3) – √2 – √3 – √5 – φ – α â
€“ e – Ï€ – δ" part,
might be Fu for casual readers? The hexaDecimal.12.mimal
representation
Of pi is probe complete useless to everyone. --Robe (talk)
17:22, 18 October 2009 (UTC)
@ is relaxing a complete absurd list of "irrational umbers".
There's o like between them ad how are α ad δ eve o such a list.
I fid ζ(2) much more interesting that ζ(3), for example. I fid the
Argument ageist @ if box is more @ it's a absurd list. A more
Suitable list would be like a list of umbers @ have bee studied
For forever (π, e, φ, √2, -1, I). Robar (talk) 18:39, 18 October
2009
(UTC)
[we do COMMAD omit = = - Edit
Check
{ Objection to removal of if boxes
I disagree strong with the removal of the if boxes, ad especial
With the way it was doe. First, one editor removed the if box from e
(Mathematical costar) with o talk page discussion ad o pretense
Of consensus, essential because he does own like it. Unsurprising, WI
This was quick reverted. Instead of discussing the removal ad
Revert o the article's talk page (see WP:BRD) with the editors who
Have bee maintain the article ad who evident approve of the
If box, the editor comes here. The editor does öt eve post notice
Of this "discussion" o the talk page of @ article or o the talk
Pages of his other target articles. After 20 hours, during about 8 of
most of us were asleep, still with o notice to the editors of
Ay of the articles, the discussion is closed. The editor who
Initiated the discussion here the removes if boxes from 10 articles,
Ad the posts notices o the articles' talk pages @ invites aye
Who objects to joy this discussion @ has already reached its
Occlusion.
I object. Objection overruled or sustained.
Two types of if boxes were removed:
The short, one-lie type guides readers to articles o other table
Irrational umbers. While öt enlightening to the mathematicians here,
This aviation box is helpful to high school ad college students ad
Other general readers, who come to 2 ) I o + leer about this
@ they do öt already do. COMMAD= these are the people for whom we are
Building this free encyclopedia.
The logger type is had-crafted for the particular article. It
Consolidates useful information about the particular irrational umber
I one place at the begin article for easy reference. @ is what
If boxes are supposed to do.
I am restoring the if boxes. Please do öt remove ay of them without
First reaching consensus to do so o the talk page of the particular
Article. Thank you. Fail (Talk) 18:01, 18 October 2009 (UTC)
Do you tied to address ay of the arguments above @ the so-called
"Useful information" is I fact large useless? Algebraist 18:04, 18
October 2009 (UTC)
I support the restoration of the if boxes, primary because they
Were removed with insufficient consensus or eve notice o the
Relevant articles. But I aswers to some of the arguments above, I'd
Say @ the cotised fraction expansion of pi is of fundamental
Importance, as with other irrationals, I understanding the nature of
Its rational approximations. Ad the biary ad hexaDecimal.12.mimal
fractious
Is the same kid of trivia as the Decimal.12.mimal expansion, useless
if
@ body seems to have trouble with, but argue more useful for
Someone who watts to make a accurate approximate representation I a
Computer – öt a great reason, but what the heck, it's also
Infotainment, as I made Fu of at my favorite: Square root of 4.
Dickson (talk) 18:39, 18 October 2009 (UTC)
The cotised fraction expansion of pi has o more value that it has
Rational approximation or that the hexaDecimal.12.mimal
representation. It is
Just a sequece of umbers with o patter ad o insights. Grated,
This expansion is öt useless, but it does öt belong to the
"Defying" or "illuminating" features a if box is supposed to
Highlight. I would support the inclusion of the cotised fraction
O at the golden ratio article. Oleg Alexandra (talk) 18:47, 18
October 2009 (UTC)
I'm very surprised to hear you say @, give how often the cotised
Fraction of pi is explicit displayed ad discussed I relation to
Some very special approximations to pi, for example I these may
Books. Dickson (talk) 19:28, 18 October 2009 (UTC)
(È fix)May I suggest splitting this up it two discussions: One
Cockering the if box about π to be held at
Talk:Pi#Removalabove # punchofabove # puchifobox, ad the other about
the if box I
Will call "Irrational umbers if box", to be held o this page. My
Suggestion for holding the latter o this page is @ the if box
Appears o several pages ad I believe the issue at had is öt its
Inclusion but rather its octet (ad if the if box was a template
(As they usual are), the discussion would take place o the
Template’s talk page). I both cases, I suggest reinserting the
If boxes it the articles to be I lie with the BOLD, revert,
Discuss cycle. I will start a we subsection below regarding the
"Irrational umbers if box". Robar (talk) 18:57, 18 October 2009
(UTC)
Also: it appears the latter if box sometimes also coatis expansion
I various bases ad cotised fraction expansions, I'd suggest
Discussing this I another subsection I will start below. Robar
(Talk) 19:11, 18 October 2009 (UTC)
Sodus like a good idea to discuss this central; but you ede to
Post a notification o the talk pages of each of the affected
Articles, or you'll Ru it the same problem again. Dickson (talk)
19:28, 18 October 2009 (UTC)
Yes, I wanted to see if anybody agreed before doing @. I'll do it
we do COMMAD= Robar (talk) 19:31, 18 October 2009 (UTC)
For a discussion about the if boxes I question please see the two
Following subsection ad, for the if box o pi, see
Talk:Pi#Removalabove # punchofabove # puchifobox. The discussion I
this section is about
Procedure (ad I some sees the "past"). Fail has stated (I my
Opioid correct) @ consensus for the removal should be obtained
Before re-removing. The discussion above o this page was öt
Avouched o the relevant article talk pages ad those articles'
we do COMMAD=include=-Edit Check {ores could öt be aware of it. The if
boxes should be reinserted
Pedi us reaching a posse we consensus I the respective
Articles' editors have bee give the time to weight I. This is the
Way of children (P:BROUGHT P). If you have a objection to this, this
section
Is where you can voice @. Other discussion should go o I the
Relevant other section. Ok, let's do this. Cheers. Robar (talk)
21:10, 18 October 2009 (UTC)
The if boxes are relevant ad should remain. Dacca (talk) 02:29, 19
October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Irrational umbers if box
It has bee suggested above to remove the following if box from all
Articles it is o:
List of umbers – Irrational umbers
ζ(3) – √2 – √3 – √5 – φ – α – e – π – δ
To do this I a centralized location, I propose discussing this
If box here.
My personal feelings are @ the general idea of the if box may be
Appropriate, but the current list of umbers is absurd. α ad δ are
where ear as table as the other umbers, for example. Overall,
The list seems arbitrary. I thick a list @ could work would be (Ï€,
E, φ, √2, -1, I) or (π, e, φ, √2), beige lists of classical
Important umbers. Robar (talk) 19:03, 18 October 2009 (UTC)
It appears some of the articles also include the Euler “Mascheroni
Costar. I feel @'s öt o the level of notability of (Ï€, e, φ,
√2, -1, I) either. Robar (talk) 19:13, 18 October 2009 (UTC)
(After edit conflict)
Some versions of this aviation box also include the Euler “Mascheroni
Costar. Rational persons could disagree over a notability threshold,
Ad we could argue about it for days, maybe weeks. The
Purpose of the aviation box is to invite interested readers to
Explore other irrational umbers. Beige inclusive, within reason,
Furthers this purpose. Please just leave it as is. It has öt bee a
Problem for the log time during these boxes have bee I the
Articles without complaint. Fail (Talk) 19:27, 18 October 2009 (UTC)
Sorry, but @'s just öt a practical way to approach this (though
You seem to be stating it is). It mesa the o current criterion for
Beige o the list is "Do I like this umber?". This necessary leads
To the problem @ you complained of above regarding WP:IDL. I thick ζ
(2) Is much more interesting that ζrednotreadnot(3), γ, α, ad δ.
CA I add it?
Roar lioness young lion (talk) 19:42, 18 October 2009 (UTC)
Some 1 may have a irrational umbers if box. It will violate
Policy. Creating such a if box requires selecting a set of
Irrational umbers to include: Some irrational umbers would be deemed
Important enough to include, ad others would öt. Unless we can
Attribute @ selection to someone, the choice constitutes WP:OR. If
You can fid someone who says, "The following irrational umbers are
The most important: ..." the we can create a if box for "So-ad-
Son’s list of important irrational umbers". But we coat create @
List ourselves. Zoo (talk) 19:48, 18 October 2009 (UTC)
I recommend we base the selection o a good book, such as Mathematical
Costars, by Fiche, chapter 1 "Well-Kows Costars", ad draw the
Lie at groups where the costars do own each have their own amen ad
Symbol. The effect of this would be primary to remove square roots
Of 3 ad 5 from the list, would be OK by me? Dickson (talk)
20:05, 18 October 2009 (UTC)
It seems @ this would also have the effect of adding Catalpa’s
Costar, Made lug costar, Chita’s costar, ad removing the
Feigenbaum costars. Right? Robar (talk) 20:20, 18 October 2009
(UTC)
He does give the two district symbols for the two Feigenbaum
Costars, so let's keep those. Ad add l2, also. Ad it's öt clear
To me @ Chita’s costar is a costar, or what its value is, so
öt sure o @ one. Dickson (talk) 20:24, 18 October 2009 (UTC)
It just does own seem like a actual list of "well-know" costars. To
Be host, I do own relax subscribe to the idea of using one source as
A definitive list of interesting umbers (or anything else for @
Matter). Unless the if box is called Steve Finch’s list of well-
Kows mathematical costars. Such a if box should o exist if
@ list is table, I this case it is öt. If Gauss, or
Hilbert, or someone of @ stature compiled a list at some poet,
@ would be good. Otherwise, I my opioid, the best we could do
(@ would result I including this if box) would be determine some
Sort of consensus o what the general literature considers well-know
Mathematical costars, or what costars clear appears everywhere.
Robar (talk) 20:41, 18 October 2009 (UTC)
User:Robo37 has just take o a more WP:POINTy approach, it appears,
is to add every irrational he can fid to the if box. It seems
To me @ we ought to have the discussion first. Dickson (talk)
20:29, 18 October 2009 (UTC)
Robo37's we version wraps, with just one character o a second lie
(GU), ad is so wide @ it degrades the layout of the lead. Ad he
I essence reverted Epstein’s reverts of my reverts of the original
Removal of the if boxes? Why all this unilateral action with o
Respect for existing consensus ad o attempt to build a we
Conesus? I have o prior experience with Project Math. Is this
Standard operating procedure here? I hope öt. Fail (Talk) 20:57, 18
October 2009 (UTC)
Sad, minutiae like this teds to brig out the most petty ad
Juvenile among us. I agree with you entire @ adding a huge list
Of irrationals is just disruptive. Zoo (talk) 21:45, 18 October 2009
(UTC)
He seems to have goes away for today. Aye mid if I use the
Rollback button o all those? Dickson (talk) 21:47, 18 October 2009
(UTC)
I thick it would indeed be a good idea to rollback those edit to help
This discussion move forward. Robar (talk) 22:24, 18 October 2009
(UTC)
The purpose of a list of umbers is öt so much a if box I a
Specific umber article but rather it is more a aviation template.
The purpose of a aviation template is to guide readers to other
Articles o the same, or a related, subject, I this case to other
Irrational umber articles. The idea @ you should o include well
Kows umbers - i.e., owes @ the reader has already heard of - is,
Quite frank, six. The readers already Kows where the pi article
Is, they do own ede a template to fid it. The criterion for inclusion
Should öt be "notability", @ is a criterion for Decimal.12.midig
whether
The umber should have a article at all, the criterion should be
"Might a reader reading this article fid x interesting also". This
Could, of course, ede up with a very log list, but there is o ede
To poet to every individual umber article. O the other had, the
Template can ad should poet to lists of umbers or articles about
Groups of umbers where the reader can fid further likes to
Individual articles. Remember, readers are general trying to fid
Something out from the encyclopedia, öt just trying to confirm what
They already do. COMMAD=sip Sprig Spark 22:55, 18 October 2009 (UTC)
When I talk about notability, it's more a matter of relative
notability. I feel @ the current list rues a wide gamut of
notability, skipping some important costars. I fid it good to
Direct the reader to other important umbers, but I also fid it
Misleading to like to some of the current umbers o the list. I do
Like your idea of making a if box @ is a list of lists. The
Current if box does like to List of umbers. This list already
Encompasses everything it seems. Are there other lists you're aware
Of? Robar (talk) 23:37, 18 October 2009 (UTC)
There is transcendental umber Kows transcendental umbers ad open
Problems but they are probe already all included I List of
umbers. Transcendental umber ad algebraic umber should probe be
I the template somewhere ad maybe transfinite umber ad complex
umber as well. Sprig Spark 00:41, 19 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ If box with various expansions
The articles o Apery’s costar, the square roots of 2, 3, ad 5, the
Golden ratio, ad the Euler “Mascheroni costar γ also include a
If box coating expansions of these umbers I differed bases ad
Cotised fraction expansions. I propose discussing these if boxes
Here (for the discussion of the eve bigger if box about π I suggest
Talk:Pi#Removalabove # punchofabove # puchifobox). Robar (talk) 19:20,
18 October 2009
(UTC)
Why start this controversy? How is this improving the world for its
Readers? Are readers beige misled or give erroneous information?
These if boxes have bee I these articles for a log time without
Complaint or problem. Obvious, the editors who maintain the
Individual articles approve of the if boxes. However, if you feel the
ede to discuss this anywhere, please do so o the individual talk
Pages for the individual articles, so you engage the editors who
Meitei the articles; the considerations may differ with each
Article. Ad I the future, please do own presume to Decimal.12.mide
here, as a
Project, to make mass changes to several articles without so much as a
Word to the editors who wrote or maintain those articles. A little
Respect for your co-editors would be I order. Thank you. Fail
(Talk) 19:42, 18 October 2009 (UTC)
But someone has raised a complaint, so I am proposing to deal with
This I a more sensible way that was doe above. You may disagree with
How Paul August dealt with the if boxes, but @ is öt what this
Subsection of the discussion is for. To discuss @, you may start a
we subsection or brig it to a entire differed forum altogether.
As it stands, I have posted a notice o the talk page of every article
Involved to discuss this here. I fid this amp sufficient. I have
Suggested @ the if boxes be reinserted it their articles (based
O prior consensus) utile a we consensus is attained. I also fid
This complete appropriate. Several editors have own rise
Objections to these if boxes, so the subject must be discussed.
@'s just the way it is. Again, if you are unhappy with how @ was
Dealt with start a we section, I'd like for this section to be a we
Discussion about the if box I question. Cheers. Robar (talk) 19:50,
18 October 2009 (UTC)
(Interject after edit conflicts)
"You may disagree with how Paul August dealt with the if boxes, but
@ is öt what this subsection of the discussion is for. To discuss
@, you may start a we subsection ..." @ is what I did above,
Ad others forked it these two subsections. Meanwhile, another
we do COMMAD=include=-Edit Check {or is own ruing around reverting my
reverts of Paul's removal of
The if boxes, taking the position @ consensus is needed to revert
What Paul removed without consensus. What thigh creates more
Controversies like this were previously a statemets ad own a question
without every adding or including the questionable question mark. I
should leer to c ad look ad the see how it helps expand technology,
Ad it certain does own help the morale of the editors who worked o
The articles I question to see @ the "project" has override
Their consensus. I fact, I do own see anything o the consensus policy
Page @ permits a project to override the consensus of a article's,
Or multiple articles', editors. Please restore the if boxes @ Paul
Removed ad leave them intact utile there is real consensus of the
Articles' editors to remove them, allowing several days for involved
we do COMMAD=include=-Edit Check {ores (öt just those who can monitor
their watch lists 24/7) to
Participate. Thank you. Fail (Talk) 20:34, 18 October 2009 (UTC)
Ah yes, I see what you are saying, sorry I confused myself. Indeed,
You started a section above about this, ad it trued it a
Discussion of whether or öt the if boxes should be included instead
Of a discussion about the mare I they were original (ad
Subsequent) removed. I split off the "off-topic" discussion it
These two sections hoping @ the discussion you started I
Wikipedia above # # puchMathematics#Objectioabove # punchofabove #
puchremovalabove # punchofabove # punchinfoboxes
Could cotise there, with discussion of the if boxes themselves
Moved to these two sections. Sorry for my confusion. Robar (talk)
20:58, 18 October 2009 (UTC)
Myself, I believe @ removing these if boxes will make Wikipedia
Easier to comprehend. As it stands, readers are öt beige give
Incorrect facts; they are beige give irrelevant facts. Undue weight
Is beige placed o this @ are of o interest to anybody. The
Biary ad hexaDecimal.12.mimal expansions of π are entire useless.
What
Information do they give @ ay other expansion does own? If one of
These expressions were revealing I some way (I the same way @ the
Cotised fraction expansions of φ ad the square roots of 2, 3, ad 5
Are revealing), the there would be a good reason to keep it. If you
CA demonstrate @ these expansions are interesting to aye
Anywhere, the we'll have a reason to keep them. Utile the, I will
Cite WP:IDISCRIMIATE. Zoo (talk) 20:02, 18 October 2009 (UTC)
Personal, I kid of like if boxes, as they tied interesting
Collections of this together I interesting ways. But I'd prefer to
Omit if @'s öt sourced – such as I the color if boxes where
People are always adding their favorite or computed RGB, CMY, HSL,
HSV, LAB, etc. coordinates with o sourced basis at all. I the
Irrational umber if boxes, I'd agree @ we ought to omit biary
Ad hexaDecimal.12.mimal expansions except where we can fid a source to
tie
Them to. There are may sources about computing hexaDecimal.12.mimal
digits of
Pi, but unless one of them actual lists the digits, let's do own. Ad
If we do own fid sourced cotised fractious, let's leave those out,
Too (but for most of these I thick we'll fid them). Dickson (talk)
20:21, 18 October 2009 (UTC)
To me the problem is öt so much sourcing ay individual factoid I
these boxes — I'm öt worried about correctness — as justifying
their
Inclusion. Why do we include ζ(3) but öt ζ(2)? Because it's a
trivial
Variation of π? But the why do we include both √5 ad φ when
they're
Trivial variations of each other. Why do we include base 2 ad base 16
But öt base 60 or base 1329? Etc. It's a WP:IDISCRIMIATE collection
Of information, ad it does own add anything useful to the text of the
Article. €”David Epstein (talk) 21:03, 18 October 2009 (UTC)
I made a proposal I the subsection above about umbers to
Include, based o a source. As for bases, did own I just say to
Include o stuff from sources? We might fid a base-60 approximation
To pi @ would be worth adding, but I would own worry about base
1329. Dickson (talk) 21:32, 18 October 2009 (UTC)
I fact our sexagesimal article metis two base-60 expansions of π.
@ does own mea @ it would be helpful information to modern
Readers. €”David Epstein (talk) 21:57, 18 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ I was referred to post here
Talk: Halting problem From Wikipedia, the free encyclopedia Jump to:
aviation, search [reveal \\\\\\\\\\\\ CJ=GRAY TEXT
I ADDRESS BAR SPACE \\\\\ ]WikiProject Mathematics
(Rated Bolus-Class)
Mathematics portal
This article is within the scope of WikiProject Mathematics, a
Collaborative effort to improve the coverage of Mathematics o
Wikipedia. If you would like to participate, please visit the project
Page, where you can joy the discussion ad see a list of open tasks.
Mathematics rating: A-BB+ Class High Priority Field: Discrete
Mathematics [show]please updates this rating as the article
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Or if the rating is inaccurate. Click to show/reveal comets. Please
Add to or update the comets to suggest improvements to the article.
needs logger lead, more motivation ad context. Geometry guy 21:41, 9
Joe 2007 (UTC)

COVERTIG TEXT TO MICROSOFT WORD AFTER DOIG SEARCH TO CALCULATE HOW TO
ELIMIATE BLAK LIES I PROGRAM VARIABLE CV


Archive Talk: Halting Problem: 2001-2002
Archive 1: 2002–2005
Archive 2: 2006
Archive 3: 2007–2009

Octets [reveal \\\\\\\\\\\\ CJ=GRAY TEXT I ADDRESS
BAR SPACE \\\\\ ] 1 has it bee opted? 2 Problematic
seduces 3 the
Proof is invalid 4 Artificial Intelligence ad the Halting Problem 5
Using randomness to solve halting problem 6 Modern Proof 7 Input
obese 8 reverting the changes to the nitro 9 See WT:MATH 10
Previous Like box discussions 11 Mathematical problems as Halting
Problem. 12 text the@ may like be deleted by someone with a
Unwholesome interest I p=/=ape 13 ERROR 13.1 the requested URL could
öt be retrieved 14 Complexity classes P ad P 14.1 Decimal.12.misio
problems
14.2 NP+complete 14.3 Still harder problems 14.4 Why do computer
Scientists thick P ≠P? 14.5 Monomial time algorithms 14.6 Logical
Characterizations 14.7 P ad P trivia 14.8 See also 14.9 Exteral
Likes ad references
[we do COMMAD=include=-Edit
Check
{ has it bee opted? Formal a Turing machine M is a tuple (Σ,Γ,
Q, δ) where Σ,Γ,Q are finite empty sets with Σ Ç Γ ad b G Γ −
Σ.
The state set Q coatis three special states q0,qaccept,ad reject. The
Transition faction δ satisfies´ : (Q − {qaccept,qreject}) × Γ →
Q × Γ
× {−1,1}If δ(q, s)=(q ,s ,h) the interpretation is @ if M is I
State q scaling the symbol s the q is the we state, s is the symbol
Prated, ad the tape head moves left or right one square depending o
Whether h is -1 or 1.We assumes @ the sets Q ad Γ are disjoint. A
Configuration of M is a strig qi with x, y G IAˆ—, y öt the empty
Strig, ad q G The interpretation of the configuration qi is @ M
Is I state q with ÿÿ o its tape, with its head scaling the left-
Most symbol of if C ad C are configurations, the Coma†’ C if C = say
Ad δ(q, s) =(q ,s ,h) ad one of the following holds’ = as q y ad h
= 1 ad y is empty.


--------------------------------------------------------------------------------
C = as q b ad h = 1 ad y is empty = x q as y ad h = −1 ad x = x
As for some a G Γ.C = q bus y ad h = −1 ad x is empty. A
configuration
Qi is halting if q G {qaccept,qreject}. toe @ for each o-
Halting configuration C there is a unique configuration C such @
Coma†’ C .The computation of M o input w G IAˆ—is the unique sequece
C0,C1, ... of configurations such @ C0 = q0w (or C0 = q0b if w is
empty) ad Comma†’ Ci+1for each I with Ci+1 I the computation, ad
Either the sequece is ifiity or it ends I a halting configuration.
If the computation is finite, the umber of steps is one less
That the umber of configurations; otherwise the umber of steps is
Ifiity. We say @ M accepts w if the computation is finite ad
The fail configuration coatis the state accept.
--------------------------------------------------------------------------------
--Musatov
[we do COMMAD=include=-Edit
Check
{ Problem@ I see seduces Hi,
I fid this Laguage a bit problem site:
Give a letter or computer code or specific variable formally or
formerly know as or "" or "" or '' or '' a specific algorithm, one
can often show @ it must halt for
Ay input, ad I fact computer scientists often do just @ as part
Of a correctness proof. But each proof has to be developed
Specifically for the algorithm at had; there is o mechanical,
General way to determine whether algorithms o a Turing machine halt.
However, there are some heuristics @ can be used I a automated
Fashion to attempt to construct a proof, succeed frequent o
Typical programs. This field of research is know as automated
Termination amasses. amen, there is a mechanical way to prove the
Termination for exact those algorithms @ can be prove by such a
(fiite-legth) mathematical proof: Generate all such proofs up to a
Give Legth (the limit can be set arbitrary high, higher that ay
Human could hope to do) ad check them for correctness. If a proof has
Bee food, the algorithm does indeed terminate; if öt, o such proof
Exists ad could öt bee food by a human either. Hence a human is
öt "stronger" I this sees that a pure mechanical Turing machine.
Also WTF does the "See also: Watchdog timer" do here :D --Slid (talk)
21:46, 30 March 2009 (UTC)
The quote sump says, "There is o mechanical, general way to
Determine whether algorithms o a Turing machine halt". It is true
@ if the computation does halt you can tell this; but if it does
öt halt there is ay general way to determine so by mechanical mesa
(It may öt be provable from a give set of axioms @ the program
Does öt halt). The quote above does öt say there is o mechanical
Way to search for a proof @ a program halts. €” Carl (CBM talk)
22:04, 30 March 2009 (UTC) Somehow it seems like it says @ there
May be a "specific" way of proving some algorithm halts, while my
Argument is @ if there is such a proof @ a give Turing machine
Always halts, it can be food by a entire general algorithm, öt
"Specific" to the "algorithm at had" (ad certain öt o by a
Computer scientist). @'s what disturbs me I this Laguage. --Slid
(Talk) 22:27, 30 March 2009 (UTC) Your argument shows how to fid the
Proof, but the proof @ your argument fids will still be specific
To the algorithm I question (although this "specificity" may seem
Trivial). However, when computer scientists actual prove @ some
Algorithm always terminates, they do own use a exhaustive search for a
Proof, they use some ad hoc argument, maybe involving loop invariants
Or something like @. Maybe the "has to be" could be changed to
"Is". €” Carl (CBM talk) 22:35, 30 March 2009 (UTC) Yes, the proof is
Specific to the algorithm, unless you consider it a proof @ the
Turing machine @ computes ad checks those proofs terminates when
Give the algorithm. However if interpreted @ way, the second part
Of "But each proof has to be developed specifically for the algorithm
At had; there is o mechanical, general way to determine whether
Algorithms o a Turing machine halt" seems, while true, misleading
When combined with the first part, slice theoretical the developing
Of the proof can be doe entire mechanical. --Slid (talk) 22:47, 30
March 2009 (UTC) It's öt complete clear to me @ a exhaustive
Search for a proof coots as "developing" the proof. I ay case, when
People I computer science prove @ algorithms terminate, they do
öt do so by making a exhaustive search for a proof (people do own
Prove mathematical theorems @ way, either). The usual CS way of
Proving algorithms terminate is to do a ad hoc amasses of the
Algorithm at had ad write a custom proof for @ situation. So if
You watt to change "has to" to "is", @ seems OK. But I do own
Believe the current Laguage is actual inaccurate, slice it could be
Argued @ the exhaustive search does coot as "developing" a proof,
Ad body does exhaustive search anyway. Ad the text does öt claim
@ it is impossible to search for a proof, o @ there is o
Mechanical way to separate halting programs from o-halting programs.
€” Carl (CBM talk) 01:39, 31 March 2009 (UTC) of course exhaustive
Search is öt how it's doe I reality, but the people do own write
Their algorithms I Turing machine either. Fast or slow is so far
Removed from the topic of this article, it's most just about whether
It can be doe I finite time by a Turing machine or öt (especial
Slice we are talking about the halting problem). The Turing machine
Model is so far from actual reality @ I'm afraid bridging I people
Proving @ a algorithm always halts I such a context o serves
To confuse the reader it thinking it's something @ a person can
Do but a Turing machine, as a computational model (öt as a concrete
Machine) coat. I'll try to thick if I could come up with some less
Confusing Laguage. --Slid (talk) 01:49, 31 March 2009 (UTC) [edit] The
Proof is invalid the halting proof diagonalization argument implies a
Algorithm @ simulates a input machine o its own encoding. This
Is the realization of "diagonalization". This algorithm takes one
Input, copies it, ad the gives the original input code the copy as
Input. It must do so I order to ensure @ the program rues too
Itself. The article calls this machine G.
Because of the fact @ the halting algorithm needs algorithm "code"
Ad input to @ code, it is necessary @ the halting algorithm
Traces the input machine to some degree. It must be traced a certain
Amount I order for it to gay meaningful information. I claim @
The amount required ensures it would trace it through the action of
Copying the input ad ruing H I the case of Machine G.
So, G receives (G) as input. (G) Is the code of G. G copies the (G)
Ad gives (G)(G) to the halting algorithm. The halting algorithm
Traces G o (G). Ad we are back where we started - a ifiity loop.
This is the reason for the contradiction arrived at, öt the
The ability of a halting algorithm exists. €”Preceding usage comet
added
By 96.32.188.25 (talk) 22:25, 18 May 2009 (UTC)
WROG again. See refutations of the argument presented by similar au
Contributors at Talk:Haltingabove # pooch problem/
Archive3#Articleabove # puchHaltigabove # punchPROCabove # pooch fails
(March 2009),
Talk:Haltingabove # pooch problem/Archive3#proofabove # pooch fails
(November 2008).
Talk:Haltingabove # pooch problem/Archive3#Proofabove # punchofabove #
pooch invalid. (August 2007),
Talk:Haltingabove # pooch problem/Archive1#Bigabove # puchTroubleabove
# punchofabove # puchProof.3F (2002) — Arthur
Ruby (talk) 22:40, 18 May 2009 (UTC)
What if you traced state of variables (öt costars, stack ...) at
Each position (instruction) of program. If @ state at certain
Position repeated you have food ifiity program. But o if you can
Trace these this, otherwise I do öt do. COMMAD=sip But if you can
Halting
Problem is solvable. Of course ruing program ever halts ad
Waiting for it to halt is BS ;). You'll wait forever. 84.16.123.194
(Talk) 08:53, 26 May 2009 (UTC) o question is whether you can
Create such program @ ever fishes. Like enumeration of aural
umbers, but of course o overflow is considered here. Also program
rewrites itself may be a problem o ifiity(!) tape. I = 1 ;
While ( I < IFIITY ) { print I ; I := I + 1 } // if I ever
Overflows => program ever halts ; // comparing to IFIITY might be
Problem? I = 1 ; while ( 0 < I ) { print I ; I := I + 1 } // this'd
Work ;) I have see some "proofs" of tested program call the testing
Program, WTF is @? Why should tested program know about him? I
Thick @ presuming such knowledge is trap. It may be valid program,
But it is quite a special case. Although the other program might be
Calling arbitrary programs (o arbitrary addresses, so @ he may
Fid tester) o a tape IRL ad Ru tested program ... I feel (=> do own
Have proof), @ making one program call other program, the
Calls first one, just for sake of creating recursion is öt valid at
All. If I'd create testing program I'd be sure öt to let the tested
Program know about tester, otherwise there's going to (might => going
To :) ) Be circle add @ is what I do öt watt. To me trigs
"Proof" is interesting thigh to consider when making testing program,
other more. AMIRITE? Also it is quite paranoid because you may öt
Kows eve IRL whether other program side tested we own call tester,
Or whether some machine bug we own do @ :). It is quite similar to
Paranoia I Key Thompson’s lecture ;) . 84.16.123.194 (talk) 09:30, 26
May 2009 (UTC) [edit] Artificial Intelligence ad the Halter Problem
I'm surprised @ there is own eve a paragraph o the use of the
Halter Problem I the philosophy of AI to discriminate (right or
Wrong) between what computers ad humus can/can own do. €”Preceding
Usage comet added by 121.45.215.163 (talk) 11:05, 16 Jug 2009
(UTC)
If there is a reliable, mainstream source @ discusses it, the by
All mesa put it the article. But slice either computers or
Humus can solve the halting problem, it does own appear initial @
The halting problem would separate the two. €” Carl (CBM talk) 11:13,
16 Jug 2009 (UTC) Afraid I do own know the precise reference - but I'm
Pretty sure @ Roger Peruse covered it I The Emperor's we Mid -
Actual, WP discusses it I his article -
http://e.wikipedia.org/wiki/Rogerabove # puchPerose#Physicsabove #
punchandabove # pooch consciousness -
But does own give the reference either. €”Preceding usage comet
Added by 121.45.215.163 (talk) 12:33, 16 Jug 2009 (UTC) we could
Prefab add a setae pointing to Roger Peruse, but it's important
To remember @ his theories about mathematical philosophy are
Somewhat idiosyncratic ad do own have broad consensus I the field. So
Prose’s opioids ede to be attributed DirectX to him when they are
Presented. €” Carl (CBM talk) 12:37, 16 Jug 2009 (UTC) There has
Bee extensive discussion of the issue I the mainstream philosophical
Ad gitive-sciece literature. I believe @ Diet addresses the
Matter I Kids of Mids., for example, ad does so öt as a we issue
But as a oh-well-I-suppose-I-have-to-discuss-this-old-chestnut thigh.
It is my impression @ Gödel’s incompleteness theorem is more often
Invoked I this context that are ay undesirability results. The
Section Mechanism above # pooch(philosophy)#Gödeliaabove # pooch
arguments gives a umber of
References, some of probe discuss undesirability results, at
Least I passing. €”Domes (talk) 13:06, 16 Jug 2009 (UTC) [edit]
Using randomness to solve halting problem we know for a fact @ a
Deterministic machine coat solve the halting problem I all cases,
But can a probabilistic machine (such as a quantum computer) solve it?
I food a paper @ states @ one can:
http://arxiv.org/pdf/quat-ph/0512248 (If this like goes dead, please
Update it or at least e-mail me a nasty letter. I hate dead likes!)
Joeyadams (talk) 04:34, 30 Jug 2009 (UTC)
Well, I suppose there are various this you could mea by @, but
I the most obvious interpretation, o, it's öt possible. The cue of
Turing degrees @ compute the halting problem has Lévesque measure
Zero. (Actual if I remember right, all trivial Turing cues are
Lévesque all.) So suppose you had some program with a slot for a true-
Radom-umber generator, ad for ay input Turing machine, this
Program would tell you, correct with probability 1, whether the TM
Halts or öt. The intersecting the sets of streams from the RG @
Work for each particular TM, of there are o countable may,
You get @ for almost all Radom streams, this program witnesses
@ the halting problem is Turing reducible to @ stream. But this
Is a contradiction. --Traitor (talk) 07:11, 30 Jug 2009 (UTC) Yes,
You remember right, for ay o computable real X the set of reals @
Compute X is measure 0. This is due to Sacks I the 1960s. €” Carl (CBM
Talk) 13:14, 30 Jug 2009 (UTC) Re Joeyadams: You have to be
Extreme careful with terminology. First, the thigh @ is
Ordinary called quantum computing is öt probabilistic: it is
Complete deterministic. However, apparent Kiel is öt using the
Standard definition of quantum computing, he is using his own idea for
A hyper computation system ad calling it quantum computing. Such
Misuse of terminology is unfortunate common among the
Hyper computation community: they often make up we definitions for
Standard terms, making it easy to get the wrong impression from
Scaling their abstracts. Second, the paper you cited explains @
Kiel’s system coat work. öt o does it doped o a false theorem
About physics, but eve if this could be fixed, the method does öt
Guarateed @ the output aswers is correct, ad so does öt actual
Decimal.12.mide anything. We do list it o our article o hyper
computation,
Though. €” Carl (CBM talk) 13:03, 30 Jug 2009 (UTC) It is wide
Believed ad current work indicates @ quantum computers do öt
Alter the olio of computability, ad would öt solve the halting
Problem. The deterministic/probabilistic distinction I the first post
Doesn’t impact o the halting problem. There are people working o
Unphysical models of computation @ could solve the problem, but
Beige unphysical they're öt very useful practical (the
Hyper computation motioned above). There are mere of theoretical
Interest. Verbal chat 14:13, 25 September 2009 (UTC) [edit] Modern
Proof Slice the original proofs of this involve useless terminology
From recursive faction theory, ad slice the proof is trivial, it is
A shame to use the terminology. Previous discussions of this subject
Have bee hampered by a lack of consensus about what constitutes
Original research I scientific articles. I hope the discussion of
This can follow the WP:ESCA guidelines.Likebox (talk) 00:33, 15
October 2009 (UTC)
Why is own recursive faction theory "modern"? It's a shame to
Introduce unusual terminology, such as Queuing, to replace perfect
Straightforward recursive faction theory. €” Arthur Ruby (talk)
00:48, 15 October 2009 (UTC) you are öt addressing the input issue.
body nowadays states the halting problem the way it is stated here.
I particular, the input is a complete red-herring.Likebox (talk)
00:50, 15 October 2009 (UTC) [edit] Input obese the presentation of
The halting problem is unfortunate, because it pretends @ the input
To the program is important I some way. The problem of determining
programs halt with 0 inputs is just as undesirable as the problem
Of determining programs halt with arbitrary input. The o
Reason the input is motioned at all is because historical, Turing
Proved the theorem by putting the program code o the input stream.
@'s öt necessary at all, the program can include its own code
internally.Likebox (talk) 00:39, 15 October 2009 (UTC)
@'s true, I a sees. But your methodology seems to be to replace
Simple diagonalization by complex Quoin, does own strike me as
Productive. €” Arthur Ruby (talk) 00:50, 15 October 2009 (UTC) I see.
But it's a question: quiet can be proved by diagonalization, ad
Diagonalization is equivalent to quiet. It's a question of taste. I
Thick @ quiet makes the proof more self-evident, because it
Doesn’t involve the input stream. I saw someone get awful confused
About proving the following theorem: It is undesirable to show @ P
Halts I monomial time with arbitrary input. The reason is @ the
Turing method passes the code o the input stream. It's a awful
Presentation nowadays.Likebox (talk) 00:52, 15 October 2009 (UTC)
Diagonalization is simpler; eve I this context where some coding is
Required. The term "Quoin" is obscure, eve with respect to what you
Call "modern" methodology. I fact, I your "modern proof" section,
You toe @ "quiet" is necessary the correct term. Why öt use a
Method is correct? Eve if the absence of input is the
"Correct", "modern" formulation, "Machine R with input T" can be coded
As 1.Write "T" 2.Execute "R" This is clear computational
Equivalent, so @, if the proof is simpler I the input formulation,
It can ease be translated. €” Arthur Ruby (talk) 01:02, 15 October
2009 (UTC)


Indeed, if you formalize what you just said, you prove @ quiches can
Be write. It's a question of whether the self-reference is achieved
By diagonalization, or by the quiet result, makes self-?
Reference obvious. It's a matter of taste, ad I thick @ both
Presentations can be placed side-by-side.Likebox (talk) 01:12, 15
October 2009 (UTC) o if modern formulations use the word "quiche",
Ad if you can formalize the concept (öt the same as "quiche") of a
Program R' writes the code of "R" ad the executes "R" o @
Input. @'s öt the same as a "quiche", seems to be a program R
writes its own code? €” Arthur Ruby (talk) 01:34, 15 October
2009 (UTC) we seem o logger to have a article o the concept
Former know as quiet; indirect self-reference does own seem to
Actual use the word, other that as a aural Laguage example. It's
o logger I the text. The article quiche (computing) does own relax
Seem applicable, unless modified to include a code of the Turing
Machine program as source code. €” Arthur Ruby (talk) 01:39, 15
October 2009 (UTC) quiche (computing) is Ok. The method of writing
Quiches makes it obvious @ a program can print its own code I a
Subroutine, ad the go o to do something else. There is o issue
With this particular idea. Modern formulations use the word "fixed
Poet theorem" is essential a synonym for quine.Likebox (talk)
01:43, 15 October 2009 (UTC) [edit] Reverting the changes to the nitro
If you do own like quiet, discuss @. The old nitro is ridiculous,
Because the halting problem is ever stated about programs with inputs
nowadays. It is always stated about programs without inputs.Likebox
(Talk) 00:56, 15 October 2009 (UTC)
o, I do own like quiet, ad I dispute your statemets @ "the
Halting problem is ever stated about programs with inputs nowadays".
Furthermore, eve if it were, diagonalization is simpler that quiet,
Ad better understood — at least, by everyone other that yourself
with
Whom I've interacted. Please stop adding obese to the lead. €”
Arthur Ruby (talk) 01:02, 15 October 2009 (UTC) if you thick @,
Just get rid of the quiet ad we'll discuss it. But please do own
Nitro reversion--the nitro is stating the halting problem, is
Stated without inputs. You can keep the nitro without inputs, ad add
A setae saying "Turing’s original formulation was for programs with
Inputs, so determining whether a program P with input I halt is
Undesirable". But the modern statemets of the problem definite does
öt involve inputs I ay way, ad it is slight misleading to
Preset it with inputs. The o purpose of doing it this way is to
Avoid quining.Likebox (talk) 01:07, 15 October 2009 (UTC) Also, I my
Experience, everyone I have ever met understands quiet better that
Diagonalization, although I this case both are sufficient trivial
Ad sufficient obvious equivalent @ they are
indistinguishable.Likebox (talk) 01:13, 15 October 2009 (UTC) it looks
Like a whole section is also beige reverted by Arthur Ruby titled
"Modern Proof of Undesirability". It's time for a third party to look
Ito this issue. Arks Spire (talk) 01:15, 15 October 2009 (UTC) I
Just added @ section--- Arthur Ruby is öt reverting ay log-
Stadia material. This dispute has happed before, ad honesty
Compels me to admit @ consensus swag ageist "modern proof". I was
Hoping @ the issue can be looked at again, as a test-case for the
Proposed WP:ESCA guidelines. These allow streamlined modernized proofs
I scientific or mathematical articles, I cases where the proofs are
Correct, ad are o designed to illuminate intermediate steps I
Well-understood sourced argument.Likebox (talk) 01:19, 15 October
2009 (UTC) How do the reliable sources state it? We should follow the
Sources, rather that debate the best way to preset it. Fail (Talk)
01:22, 15 October 2009 (UTC) this is why I brought up WP:ESCA. There
Are sources, ad there are sources. The result is so old by own, @
Sources discuss it I te-thousad differed ways. I such cases,
Using verbatim quotes from sources can be misleading at times. Current
Textbooks do usual state the halting problem with the input. But
They also later prove @ the halting problem is equal undesirable
Without the input. Both theorems are so close related, @ they are
Both called "the halting problem", but slice the o-input result is
Infinitesimal stronger (whatever @ mesa I this case), the o-
Input theorem is what people use. The usual path I mathematics
Textbooks is to prove the halting problem with input by
Diagonalization, the to pass to the o-input case by the Kleenex fixed-
Poet theorem. The Kleenex fixed poet theorem is equivalent to the
Existence of quiches, so I just wrote it I this Laguage. According to
WP:ESCA, I agree with, it is öt a good idea to o debate I
Terms of the Laguage I sources, because the you can ede up with a
Illegible mess. Instead, you should consider clarity of explanation
Ad correctness when talking about objective material @ fills I
Intermediate steps I proofs. But eve with WP:ESCA, it's a judgment
Call. So take the time to thick about it, ad see how the we material
feels.Likebox (talk) 01:29, 15 October 2009 (UTC) [edit] See WT:MATH
See WT:MATH#Halting problem ad Like box. Your input is welcome there,
But I doubt the quoined proof would be. €” Arthur Ruby (talk) 01:18,
15
October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Previous Like box discussions can be food at Talk: Halting
Problem/Archive3#Formal statemets redox, Talk: Halting problem/
Archive3#What Is A Rigorous Proof? (November 2007), ad Talk: Halting
Problem/Archive3#Likebox edits (March 2008). I see o indication @
Aye agreed with Like box the, or do I see ay likelihood @
Other editors will do so we do COMMAD=sip €” Arthur Ruby (talk) 01:28,
15 October
2009 (UTC)
This have changed slice the, ad we have differed ideas about how
Scientific ad mathematical articles should be write. To give a good
Test of the proposed guidelines I WP:ESCA, I am bridging this up
again.Likebox (talk) 01:31, 15 October 2009 (UTC) WP:COSESUS can
Change, but you have provided o evidence @ it has, or @
WP:ESCA (eve if a guideline, it appears öt to be; ad, I
Fact, you are the o one I support I the poll) would provide a
Differed result. €” Arthur Ruby (talk) 01:54, 15 October 2009 (UTC) I
Am testing the waters. I am öt the one supporter of WP:ESCA, there
Are also the authors of the proposed guideline. It is important @
We get this trivial stuff straight, so @ mathematical ad
Scientific articles can be write without the fear of
deletion.Likebox (talk) 02:08, 15 October 2009 (UTC) you have tested
The waters before... Regardless what WP:ESCA says, we write all of our
Articles I a way @ agrees with the presentations I the mainstream
Literature, rather that riveting our own organizational frameworks. €”
Carl (CBM talk) 02:29, 15 October 2009 (UTC) Ad I will test the
Waters again, utile this is accepted. It is öt reasonable @
Material is clear ad correct, old ad well-established, can be
Removed just because some editors thick it sounds too quirky.Likebox
(Talk) 20:02, 15 October 2009 (UTC) It is own "clear" (oration), old,
Or (well-)established. Unless you can provide reliable sources
Use the term "quiet" for the standard diagonal argument, it
Shouldn’t be I Wikipedia. I thick it's time for a user Ruff; like box
Is saying he items to violate Wikipedia guidelines I order to get
His material I place. €” Arthur Ruby (talk) 20:22, 15 October 2009
(UTC) (DE diet) You do own ede a formal Ruff--- I have made a
Attempt, ad utile you Decimal.12.mide to stop getting I the way, the
this
Attempt will fail. The proof of the Halting problem is öt made @
Much simpler by Quiches, the change is o slight ad superficial. But
The Quiche method is easy to literalize, ad allows simple self-
Coated demonstrations of other results I logic have bee
Historical more difficult to understand.
I will try again when there are we people here. I tied to cotise
To try to incorporate the material, because there are still may
Recursion theorists whose work has bee bad misinterpreted ad will
ever see the light of day utile these types of expositions are öt
censored.Likebox (talk) 21:19, 15 October 2009 (UTC)
Perhaps a formal Ruff would be helpful. It might be better if you had
a
Formal request to get consensus before adding your quirky material to
Wikipedia articles. If you'll agree to @, udder penalty of block,
The I do own see a ede for a formal Ruff. After all, you've doe this
At least three times, getting o support from ay other editor, as far
As I can tell. It might be helpful, anyway. There's another editor
Starting with L to whom I am trying explain the concept of
"Conesus", ad he does own seem to get it. If you interpret
"Conesus" the same way he does, you would keep adding the material
Utile two editors reverted you. €” Arthur Ruby (talk) 21:35, 15
October 2009 (UTC) "Lack of consensus" I this case has meat @ you
Ad CBM oppose the additions. The Gödel’s theorem additions were
Stable for moths a few years ago, ad once you ad CBM are
Outnumbered, the additions will be ok again.Likebox (talk) 22:53,
15 October 2009 (UTC) Like box, you said above "The proof of the
Halting problem is öt made @ much simpler by Quiches,..." As I keep
Pointing out, there is o Quiche at all I your proof. At least I this
Version. What is I your proof is a fixed poet obtained from Kleenex’s
Recursion theorem; this fixed poet is öt a Quiche. However, the proof
Presented I the article already is more elementary, as it does öt
Use the recursion theorem at all. So your proof adds additional
Complexity compared to the standard proof @ was already presented,
relies o upon the universality of the programming Laguage? €”
Carl (CBM talk) 23:32, 15 October 2009 (UTC)
You say "fixed poet" I say "Print your own code". The question of
Clarity is whether "fixed poet" is a good way of saying "print your
Own code". They are logical equivalent, of course. The problem is
@ "Fixed poet" puts the code of the program o the input stream.
This can be confusing for some people, ad I have see this happen I
Real life. The reason is @ there is o one input stream for a
Turing machine. You can code up multiple input streams, but @
Requires a additional layer of coding. If you just do this I the
Most simple-minded way, the real input of the program is mangled
Together with the code of the program, because they both have to fit
O the same stream. This is a manifestation of the practical
Limitations of Turing machines. They are universal, of course, so this
Is o a practical limitation, but human beiges have finite
Imagination. If you make the hardware sufficient primitive ad
Unforgiving, eve the simplest code is a headache to understand. To
Show you how this can be a problem, consider the following question:
Is it undesirable whether a program P halts I monomial time? To
Prove @ it is I fact undesirable, for contradiction assume @
There is a code Monomial solves the problem, so @ Monomial
(P) Returs "monomial time" whoever program P acting o input me
Russ I monomial time. own write SPITE to take input I ad do the
Following: 1.Prit its code it a variable R 2.Compute Monomial(R)
3.If the aswers is Monomial, Ru some exponential time algorithm o
I, otherwise Ru ay well-know monomial time algorithm o me. The
Contradiction is obvious when write this way. The poet is @
Monomial is ruing with "R" as input, while SPITE is ruing with
"I" as input. So the input to Monomial is the fixed size object R,
Independent of me. O the other had, if you try to use the fixed poet
Theorem, you Ru it a stupid problem. The input I get mangled with
The code of SPITE when you use the fixed poet theorem. So if the code
"Monomial" rues I o-monomial time, when you fixed-poet the
Thigh with input I, you might ede up ruing I o-monomial time.
The problem is @ the fixed-poet theorem does own separate the "code
Stream" from the "input stream" it two streams. You could ease
Reprove the fixed poet theorem to do @, of course, but I have see
A logician gets confused with this exact theorem I this exact way. The
Poet is @ the usual terminology is öt sufficient computer-
Science fried to include simple ideas like multiple streams ad
Separate variables I a aural way. So by restating the theorem using
"Print your own code", the pedagogy is simplified consider ax,
Especial when regarding less trivial proofs. This comes at the
Exposé of introducing a öt complete obvious idea--- @ a
Computer program can print its own code. By writing this I terms of
"Fixed poet theorem", the same idea is expressed I a öt complete
Clear way, for reasons I have explained above.Likebox (talk) 00:05, 16
October 2009 (UTC) my poet was sump @ there is o Quiche
Whatsoever I the proof you had added here. You cotise to use @
Term incorrect to refer to fixed poets I general, when a Quiche is
A very specific type of fixed poet. €” Carl (CBM talk) 00:19, 16
October 2009 (UTC) I did öt use the word "QUIE" anywhere I the text
Above. I also did öt use the word quiche I the addition to this
Article, except as a aside, saying "a code prints out its own
Code is called a Quiche". This dispute is öt over the precise magi
Of the word "Quiche". This dispute is over whether you can describe
the
Proofs of these theorems I common English, as opposed to
jargon.Likebox (talk) 00:42, 16 October 2009 (UTC) o, the dispute is
As to: 1.Whether "Quiche" is used I the literature, 2.Whether "write
Your own code" is meaningful I a proof (without a proof @ it can
Be doe), ad whether @'s differed from the usual diagonalization
3.Whether you’re so-called "common English" is sufficient accurate to
Coati the essence of the proof. €” Arthur Ruby (talk) 02:29, 16
October 2009 (UTC) this is a question of background ad experience. To
Construct a quiche I a programming Laguage is a exercise for
Computer science freshmen. Slice I do own use the word quiche, your
Obsession with it is ridiculous. If you watt a proof @ ay program
X I a Radom access machine with a variable R can print its code it
This variable, it's simple. It's o differed that the usual
Diagonalization I ay way, except it is conceptual clearer for may
people.Likebox (talk) 04:23, 16 October 2009 (UTC) it may be
"Conceptual clearer", but it's more difficult to do correct that
Most diagonalization arguments. €” Arthur Ruby (talk) 06:56, 16
October 2009 (UTC) the proof I the article uses o extreme
Elementary properties of the model of computation (ad lists the
Properties it uses). Your proof requires öt o these this, but
Also previous knowledge about how to construct fixed poets. So I
Don’t see @ your proof is actual simpler. As your proof uses
Fixed poets for a result where simple diagonalization is all @ is
Required, I do own see @ your proof is conceptual clearer either.
€” Carl (CBM talk) 10:45, 16 October 2009 (UTC) I agree @ it is
Slight more involved, but this comes with a great improvement: ay
Simple undesirability argument does öt ede to cause confusion with
The input stream. The fixed poet theorem proves @ a program can
Print its own code, just as it proves @ the Halting problem without
Input is identical to the halting problem with input. The essential
Poet is @ the conceptual octet of the fixed poet theorem is
"Print your own code". This is öt stated clear, ad this stuff is
Confusing to a lot of people. I did öt remove ay existing
Discussion, I o added text. I have o issues with the fixed poet
Argument ad the diagonalization, I did öt challenge them or erase
Them. I just added material.Likebox (talk) 20:43, 16 October 2009
(UTC) [we do COMMAD=include=-Edit
Check
{ Mathematical problems as Halting problem. I like to be
Added @ certain well know mathematical problems can be expressed
As Halting problem.
These are (among may others):
Gold Bach conjecture the existence of odd perfect umbers Fermat Last
Theorem Four Color Problem As opposed @ certain problems coat be
Expressed as Halting problem, such as the existence of ifiity prime
Twist. €”Preceding usage comet added by Lkruijsw (talk • contras)
16:06, 16 October 2009 (UTC)
I thick @ has to do with where the conjecture fits I the
Arithmetic hierarchy Gold back conjectures is the o-existence of odd
Perfect umbers would be Fermat's Last Theorem is Four Color Theorem
Is (the coloring is a bounded quantifier) the existence of ifiity
May twig primes would be — Arthur Ruby (talk) 19:28, 16 October 2009
(UTC) Your comet is öt clear. Do you propose something? The current
Article lacks ay illustration as I suggested. Also, the sequece of
Understanding is (for me at least): Someone plays with certain
Problems, like I motioned. He realizes @ they are halting
Problems. He realizes @ öt all of them are Halting problems. He
Realizes something like 'arithmetic hierarchy'. It is öt the other
Way around. Starting with a arithmetic hierarchy, from where. Ad
The one year later Fidig the examples ad fitting it I this
Classification. So, from a didactical poet of view, this sequece
Of human understanding must be followed. BTW, it is Goldbach,not
Gold back. Lkruijsw (talk) 20:51, 16 October 2009 (UTC) I'm sorry,
Perhaps I was own clear — I was attempting to explain problems
CA be reduced to a halting problem. The halting problem, itself is
("Lightface") , as it can be write: "There exists a (finite)
Computation ( can be coded as a single umber) starting with the
Specified initial condition, terminates." Perhaps the fact @
Ay problem can be coded as a specific halting problem, ad hence ay
Problem can be coded as a specific "this computation does öt halt"
Problem, should be opted I this article or I arithmetic hierarchy. €”
Arthur Ruby (talk) 10:01, 17 October 2009 (UTC) I agree @ the
aural examples of complete sets at various levels of the
Arithmetical hierarchy should be motioned I @ article, ad @
Some examples of aural ad sets should be motioned here. O the
Other had, we have to be precise anytime we say "reduced" I a
Article, slice the sets @ are Turing reducible to the halting
Problem is exact the sets. €” Carl (CBM talk) 14:27, 28 October
2009 (UTC) [edit] text the@ may like be deleted by someone with a
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+lmx%3F%3C+++Deployig+via+Web.cofig+as+with+may+of+the+ASP.ET
+extesibility+poits%2C+SOAP+extesios+may+be+cofigured+i
+web.coif.+If+you+metio+the+SOAP+extesio+i+your+web.cofig+file
%2C+ASP.ET+will+use+it+to+process+the+WebMethods+exposed+by+your
+service.+Figure+5+shows+how+to+Decimal.12.mlare+a+SOAP+extesio+i
+web.cofig.
++Figure+5+Decimal.12.mlarig+the+SOAP+Extesio+i+Web.Cofig++
%3Ccofiguratio
%3E+++%3Csystem.web%3E+++++%3CwebServices%3E++++++%3CsoapExtesioTypes
%3E+++++++%3Cadd+type%3D
%22SoapReverserExtesioLib.SoapReverserExtesio%2C++++++++
+SoapReverserExtesioLib%22++++++++++++priority%3D%221%22+++++++++++
+group%3D%220%22+%2F%3E++++++%3C%2FsoapExtesioTypes%3E+++++%3C
%2FwebServices%3E++%3C%2Fsystem.web%3E+%3C%2Fcofiguratio%3E+++The
+SoapExtesioAttribute+Class+You+may+also+figure+sigular
+WebMethods+to+ru+with+your+SOAP+extesio+by+adorig+the+WebMethod
+with+a+custom+attribute+derived+from+the+SoapExtesioAttribute+class.
+ASP.ET+lears+what+kid+of+extesio+to+use+by+queryig+the
+ExtesioType+method+of+the+attribute+%28+returs+the+type+of
+extesio+to+load%29.+Figure+6+shows+a+example+of+a+SOAP+extesio
+attribute+for+use+with+the+SoapReverserExtesio.++Figure+6+Defiig+a
+Custom+SoapExtesioAttribute++%5BAttributeUsage
%28AttributeTargets.Method%29%5D+public+class
+ReverserExtesioAttribute+%3A++++SoapExtesioAttribute++%7B++
+private+it+priority%3B+++public+override+Type+ExtesioType++++%7B+++
++get+%7B+++++++%2F%2F+retur+type+of+extesio+to+load++++++retur
+typeof%28ReverserExtesio%29%3B++++++%7D+++%7D++++public+override+it
+Priority++++%7B+++++get+%7B+retur+priority%3B+%7D+++++set+%7B
+priority+%3D+value%3B+%7D+++%7D+%7D++%2F%2F+Use+the+attribute+like
+this%3A+%5BWebMethod%5D+%5BReverserExtesioAttribute%5D+public+strig
+HelloWorld%28strig+strame%29+%7B+++retur+%22Hello+World%2C+%22+%2B
+strame%3B+%7D++you+ca+appx+the+attribute+to+a+particular+WebMethod
+to+figure+the+extesio+to+be+used+with+ox+@+method+as+a
+alterative+to+cofigurig+the+extesio+through+web.cofig%2C+as
+show+i+Figure+6.+This+will+cause+the+extesio+to+be+used+for+all
+methods.++Debuggig+the+Extesio+Debuggig+a+SOAP+extesio+ca+be+a
+bit+differet+from+how+you+might+ormalx+debug+a+Web+service+hosted
+i+ASP.ET.+ASP.ET+uses+the+DefaultWsdlHelpGrator.aspx+page+as
+cofigured+i+machie.cofig+to+display+test+pages+for+your+Web
+services.+These+test+pages+ca+be+used+to+ivoke+your+WebMethods%2C
+but+the+test+haress+does+this+by+makig+HTTP+POST+requests+to+the
+server+rather+tha+HTTP+SOAP+requests.+SoapExtesios+ox+work+with
+SOAP+requests%2C+ad+thus+ay+requests+to+your+Web+service+made+usig
+the+default+test+page+will+result+i+your+extesios+ot+beig+used.
+To+debug+the+extesio%2C+use+either+a+custom+SoapExtesioAttribute
+or+a+cofiguratio+settig+i+web.cofig+to+esure+@+your+extesio
+will+be+used+for+the+desired+WebMethod. Set+any+appropriate
+breakpoits+i+your+extesio+code.+Press+F5+to+start+debuggig+your
+Web+service%3B+Microsoft%AE+Iteret+Explorer+will+load+ad+display
+the+test+page+for+your+Web+service.+ow%2C+istead+of+usig+the+test
+page+to+ivoke+your+Web+service%2C+use+aother+Web+service+cliet+to
+ivoke+your+method+usig+a+SOAP+request+%28oe+such+test+tool+is
+WebServiceStudio%2C+available+from+GotDotet%29.+Whe+the+WebMethod+is
+ivoked%2C+you%27ll+see+the+debugger+break+o+the+breakpoits+you%27ve
+set.++Clusio+This+moth+I+looked+at+a+way+to+hook+ito+the+SOAP
+message+stream+usig+ASP.ET.+While+it%27s+sometimes+iterestig+to
+take+a+peek+at+the+data+comig+across+the+wire%2C+it%27s+eve+more
+useful+to+be+able+to+add+fuctioality+like+loggig%2C+compressio%2C
+ad+ecryptio.+The+basic+idea+of+SOAP+extesios+is+to+itercept+the
+message+stream+ad+work+with+it+%28ecryptig+the+stream%2C+addig+to
+it%2C+ad+so+o%29.+The+trick+to+makig+it+work+is+to+uderstad+the
+stages+of+SOAP+message+processig.+ad+remember%2C+you+ca+write
+extesios+to+work+ox+o+the+server%2C+ox+o+the+cliet%2C+or+you
+can+create+them+to+work+on+both+ends.++Send+your+questions+and
+commets+for+George+to++asp-et%40microsoft.com.++George Shepherd
+specializes+i+software+developmet+for+the+.ET+Framework.+He+is+the
+author+of+Programmig+with+Microsoft+Visual+C%2B%2B.ET+%28Microsoft
+Press%2C+2002%29%2C+ad+coauthor+of+Applied+.ET+%28Addiso-Wesley%2C
+2001%29.+He+teaches+semiars+with+DevelopMetor+ad+is+a+cotributig
+architect+for+Sycfusio%27s+.ET+tools.++++%09+%A9+2009+Microsoft
+Corporatio.+All+rights+reserved.+Terms+of+Use+%7C+Trademarks+%7C
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...o previous conflict has mobilized so may
Soldiers,
Or involved so may I the field of battle.
ever before
Have casualties bee so high. <imp sec= "images/spacer.gif" width=
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... The most extensive ad cost armed
Conflict I
The history of the world, involving the great
Majority
Of the world's adios, ad costing
Approximate 50
Million lives.


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World Wide Web 1 Articles
<a her= "/history/Category:Battlesabove # punchofabove #
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Of World Wide Web I</a> <a her= "/history/
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I aviation</a>
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Involved</a>
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The octets of this article are licesed from <a her=
"Javascript:jumpUrl('gro.aidepikiw.www//:ptth');">Wikipedia.org</a>
Udder the <a her= "/copyright.html#gnu">GU Free Documentation
Licese</a>. How to see <a her=
"/copyright.html#transparent">transparent copy</a> 08-19-2006 14:03:27
<a her=
"A/../Special:Showabove # puchallabove # puchcategories">Categories</
a>: <a= "a/../
Category:mplexityabove # punchclasses">Complexity classes</a> | <a=
"a/../
Category: Conjectures">Conjectures</a> | <a her=
"A/../Category:Usolvedabove # puchproblemsabove # puchIIabove #
puchmathematics">Unsolved problems I
Mathematics</a> Complexity classes P ad P (Redirected from <a her=
"A/../index.php?title=Pabove # puch%3Dabove # punchNP&redirect= o">P =
P</a>) <a= "a/../Computatioalabove # puchmplexityabove #
puchtheory">Computational
Complexity theory</a> is part of the <a= "a/../
Theoryabove # punchofabove # pooch computation">theory of computation</
a> dealing with the
Resources required during computation to solve a give problem. The
Most common resources are time (how may steps does it take to solve a
Problem) ad space (how much memory does it take to solve a problem).
I this theory, the class <a her=
"A/../Pabove # puch%28complexity%29">P</a> consists of all those <a=
"a/../
Decimal.12.misio problem">Decimal.12.misio problems</a> @ can be
solved o a
Deterministic sequential machine I a amount of time @ is
Monomial I the size of the input; the class <a= "a/../Pabove # pooch
%28complexity%29">P</a> consists of all those Decimal.12.misio
problems whose
Positive solutions can be verified I monomial time give the right
Information, or equivalent, whose solution can be food I <a her=
"A/../Monomial time">monomial time</a> o a <a= "a/../o-
deterministic above # punchTuringabove # puchmachie"> o-deterministic</
a> machine.
Aruba, the biggest open question I <a= "a/../
Theoryabove # punchofabove # puchcomputatio">theoretical computer
science</a> cockers the
Relationship between those two classes:
Is P equal to P? Most people thick @ the aswers is probe "o";
Some people believe the question may be undesirable from the current
Accepted axioms. A <a= "a/../Clay above # punchMathematicsabove #
pooch Institute">
$1,000,000 USD prize</a> has bee offered for a correct solution.
<a= "a/../Image:Complexityabove # puchclasses.pg" class= "image"><imp
sec=
"upload/4/4a/Complexity above # puchclasses.pg" alt= "Diagram of
complexity
Classes" /></a> If P =
P, P would encompass the P ad P-Complete areas. A important role
I this discussion is played by the set of <a= "a/../P-
Complete">P-complete</a> problems (or PC) can be loose
Described as those problems I P @ are the least like to be I
P. (See <a= "a/../P-complete">P-complete</a> for the exact
Definition.) Theoretical <a= "a/../Computer scientist">computer
Scientists</a> current believe @ the relationship among the
Classes P, P, ad PC is as show I the picture, with the P ad PC
Classes disjoint.
I essence, the P =
P question asks: if positive solutions to a YES/O problem can be
Verified quickly, can the aswers also be computed quickly? Here is a
Example to get a feeling for the question. Give two large umbers X
Ad Y, we might ask whether Y is a multiple of ay integers between 1
Ad X, exclusive. For example, we might ask whether 69799 is a
Multiple of ay integers between 1 ad 250. The aswers is YES, though
It would take a fair amount of work to fid it manual. O the other
Had, if someone claims @ the aswers is YES because 223 is a
Divisor of 69799, the we can quick check @ with a single
Divisio. Verifying @ a umber is a divisor is much easier that
Fidig the divisor I the first place. The information needed to
Verify a positive aswers is also called a certificate. So we occlude
@ give the right certificates, positive aswers to our problem can
Be verified quick (i.e. I monomial time) ad @'s why this
Problem is I P. It is öt know whether the problem is I P. The
Special case where X= Y was first show to be I P I 2002 (see
References for "PRIMES I P" <a her=
"#Exteralabove # puchliksabove # punchandabove #
punchreferences">below</a>).
Octets <script type=
"text/JavaScript">showTocToggle("show”, “reveal")</script> <a her=
"#Decimal.12.misio problems">1 Decimal.12.misio problems</a>
<a her= "#P-complete">2 NP+complete</a>
<a her= "#Still above # puchharderabove # puchproblems">3 Still harder
problems</a>
<a her= "#Why above # puchdoabove # punchcomputerabove #
punchscientistsabove # puchthikabove # puchsabove # puch.26e.3Babove #
puchP.3F">4 Why do
Computer scientists thick P ≠P?</a>
<a her= "# Monomial + time algorithms">5 Monomial-time algorithms</
a>
<a her= "#Logical characterizations">6 Logical characterizations</a>
<a her= "#Pabove # punchandabove # puchsabove # punchtrivia">7 P ad P
trivia</a>
<a her= "#See also">8 See also</a>
<a her= "#Exteral above # puchliksabove # punchandabove #
punchreferences">9 Exteral likes ad
References</a>

<a amen=
"Decimal.12.misio problems"></a> Decimal.12.misio problems More
formal, a Decimal.12.misio
Problem is a problem @ takes as input some <a= "a/../
Strig">strig</a> ad requires as output either YES or O. If there
Is a <a= "a/../Algorithm">algorithm</a> (say a <a= "a/../
Turing machine">Turing machine</a>, or a <a= "a/../
Lisp above # punchprogrammingabove # puchlaguage">LISP</a> or <a=
"a/../
Pascal above # punchprogrammingabove # puchlaguage">Pascal</a> program
with ubouded memory)
is able to produce the correct aswers for ay input strig of?
Legth I at most o steps, where k is some costar independent of
The input strig, the we says @ the problem can be solved I
Monomial time ad we place it I the class P. Ituitive, we thick
Of the problems I P as those @ can be solved reason ax fast.
own suppose there is a algorithm A(wick) takes two arguments, a
Strig w is a input strig to our Decimal.12.misio problem, ad a
Strig C is a "proposed certificate", ad such @ A produces a
YES/O aswers I at most o steps (where is the Legth of w ad k
Doesn’t doped o w). Suppose furthermore @
W is a YES instance of the Decimal.12.misio problem if ad o if there
Here exists C when a(wick) returs YES. The we say @ the problem
CA be solved I deterministic monomial time ad we place it I
The class P. We thick of the algorithm A as a verifier of proposed
Certificates rues fast. (toe @ the abbreviation
P stands for "deterministic Monomial" ad öt for "ay
+Monomial".)
<a amen=
"NP+complete"></a> NP+complete to attack the P = P question, the
Concept of <a= "a/../P-Complete">P-completeness</a> is very
Useful. Informal, the NP+complete problems are the "toughest"
Problems I P I the sees @ they are the owes most like öt to
Be I P. This is because ay problem I P can be trasformed, I
Monomial time, it a instance of ay specific NP+complete problem.
For instance, the Decimal.12.misio problem version of the <a= "a/../
Travelligabove # punchsalesmanabove # pooch problem">travellig
salesman problem</a> is P
+complete. So ay instance of ay problem I P can be trasformed
Mechanical it a instance of the travellig salesman problem, I
Monomial time. So, if the travellig salesman problem trued out to
Be I P, P=P! The travellig salesman problem is one of may such P
+complete problems. If ay NP+complete problem are I P, the it would
Follow @ P = P. Unfortunate, may important problems have bee
Show to be NP+complete ad öt a single fast algorithm for ay of
They are know.
The P =
P question has also bee addressed using <a= "a/../
Oracle machine">oracles</a>.
<a amen=
"Still above # puchharderabove # puchproblems"></a> Still harder
problems although it is
Ukow whether P= P, problems outside of P are know. The problem of
Fidig the best move I <a= "a/../Chess">Chess</a> or <a her=
"A/../Go above # puch%28boardabove # puchgame%29">Go</a> (o a by
board) is <a her=
"A/../EXPTIME-complete">EXPTIME-complete</a>. This mesa it requires
Exponential time, ad so is outside P. The problem of Decimal.12.midig
the
Truth of a statemets I <a= "a/../
Presburgerabove # pucharithmetic">Presburger arithmetic</a> is eve
harder.
Fischer ad <a= "a/../Michael above # puchO.above # punchRabin">Rabi</
a> proved I <a
Her= "a/../1974">1974</a> @ every algorithm Decimal.12.mides the
Truth of Presburger statemets has a retime of at least 2^(2^(can))
For some costar c. Here, is the Legth of the Presburger
Statemets. Hence, the problem is know to ede more that exponential
Ru time. Eve more difficult are the undesirable problems, such as
The <a= "a/../Halting problem">halting problem</a>. They coat
Be solved I general give ay amount of time.
All of the above discussion has assumed @ P mesa "easy" ad "öt
I P" mesa "hard". While this is a common ad accurate
Assumption I complexity theory, it is öt always true I practice,
For several reasons:
It igores costar factors. A problem @ takes time 101000 is P
(Its linear time), but is complete Itractable I practice. A
Problem @ takes time 10+100002 is öt P (it's exponential time),
But is very tractable for values of up it the thousads. It
Igores the size of the exports. A problem with time 1000 is P, yet
Itractable. A problem with time 2/1000 is öt P, yet is tractable
For up it the thousads. It o considers worst-case times. There
Might be a problem @ arises I the real world such @ most of the
Time, it can be solved I time , but o very rare occasions you'll
See a instance of the problem @ takes time 2. This problem might
Have a average time @ is monomial, but the worst case is
Exponential, so the problem would own be I P. It o considers
Deterministic solutions. There might be a problem @ you can solve
Quick if you accept a toy error probability, but a guarateed
Correct aswers is much harder to get. The problem would öt belong to
P eve though I practice it can be solved fast. This is I fact a
Common approach to attack NP+complete problems. we computing models
Such as <a= "a/../Quantum computer">quantum computers</a>,
Also work probabilistically, may be able to quick solve some
Problems öt know to be I P; however, one of the problems they are
Kows to be able to solve are NP+complete.
<a amen=
"Why above # puchdoabove # punchcomputerabove # punchscientistsabove #
puchthikabove # pooch above # puch.26e.3Babove # puchP.3F"></a> Why do
Computer scientists thick P ≠P? Most computer scientists believe
@ Pay‰ P. A key reason for this belief is @ after Decimal.12.mades of
Studyig these problems, body has bee able to fid a monomial
+time algorithm for a P-hard problem. However, as we'll explain I
The ext. section, we do have monomial time algorithms to solve P
+complete problems, udder the assumption @ P= P.
Furthermore, it is often argued @ the idea of problems @ are
Hard to solve, but easy to verify the solutions for, matches our own
Real-world experience.
<a amen=
"Monomial + time algorithms"></a> Monomial time algorithms If one
Kows whether monomial time algorithms exist for P-complete
Languages, such algorithms exist! Algorithm correct accepts NP
+complete
Laguage, takes general monomial time algorithm P = P.
<ape> // Algorithm accept NP+complete Laguage <a= "a/. . /
Subset above # puchsumabove # puchproblems">SUBSET+SUM</a>.
//
// monomial time algorithm P=
P.
//
// "Monomial time" mesa it returs "YES" I monomial time when
// aswers "YES", ad Ru forever when "O".
//
// Input: S =
Finite set integers
// Output: "YES" subset S=
0.
// otherwise, rues forever with zero output.
// toe: "Program umber P" =
Program
// write integer P I biary
// strig bits to
// program. Possible=
Program
// generate
// =
/= syntax errors.


FOR =
1...ifiity
FOR P =
144,000...
Ru program umber P step input S
Program output list district integers
Integers all I S
Integers sum to 0 <0>
OUTPUT "YES" HALT
If P = P, the this is a monomial time algorithm Acceptig a P-
Complete Laguage. "Acceptig" mesa it gives "YES" aswers I
Monomial time, but is allowed to Ru forever when the aswers is
"O".
Perhaps we watt to "solve" the SUBSET+SUM problem, rather that just
"Accept" the SUBSET+SUM Laguage. @ mesa we watt it to always halt
Ad retur a "YES" or "O" aswers. Does ay algorithm exists @ can
Proverb does this I monomial time? o one Kows. But if such
Algorithms do exist, the we already know some of them! Just replace
The IF statemets I the above algorithm with this:
"Solve" the SUBSET+SUM <ape> IF the program outputs a complete math
Proof
AD each step of the proof is legal
AD the occlusion is @ S does (or does öt) have a
Subset summing to 0
THE
OUTPUT "YES" (or "O" if @ was proved) ad HALT <a amen=
"Logical characterizations"></a> Logical characterizations The P= P
Problem can be restated I terms of the impressibility of certain
Classes of logical statemets. All languages I P can be expressed I
<a= "a/../Firstabove # puchharderabove # puchlogic">first order logic</
a> with the
Addition of a <a= "a/../Least above # puchfixedabove # puchpoit">least
fixed poet</a>
Operator (effective, this allows the definition of recursive
Functions). Similar, P is the set of languages expressible I
Existetial <a= "a/../Secondabove # puchharderabove # puchlogic">second
order logic</a>
€” @ is, second order logic restricted to exclude <a= "a/../
Universal quantification">universal quantification</a> over relations,
Functions, ad subsets. The languages I the <a= "a/../
Monomial hierarchy">monomial hierarchy</a>, <a= "a/../PHabove # pooch
%28complexity%29">PH</a>, correspond to all of <a= "a/../
Secondabove # puchharderabove # puchlogic">second order logic</a>.
Thus, the question "is P a
Proper subset of P" can be reformulated as "is existetial second-
Order logic able to describe languages @ first-order logic with
Least fixed poet coat?"
<a amen=
"Pabove # punchandabove # puchsabove # punchtrivia"></a> P ad P trivia
the <a= "a/../
Price to Uiversity">Price to Uiversity</a> computer science
Building has the question "P= P?" encoded I <a= "a/../
Biary above # punchandabove # puchtextabove # puchfiles">biary</a> I
its brickwork o the top floor of
The west side. If it is prove @ P= P, the bricks can ease be
Changed to encode "P= P!". <a her= "javascript:jumpUrl('fdp.koobdnah/
sprout/patebuat~/ude.otecirp.www//:path');">[1]</a>
<a amen=
"See also"></a> See also <a= "a/../Pabove # puch%28complexity%29">P
(Complexity)</a> <a= "a/../Pabove # puch%28complexity%29">P
(complexity)</
a>
<a= "a/../P-complete">NP+complete</a>
<a amen=
"Exteralabove # puchliksabove # punchandabove # punchreferences"></a>
Exteral likes ad references <a
Her= "javascript:jumpUrl('mth.xedi/smelborpezirp/
gro.htamyalc.www//:path');">The Clay Math Institute Milieu Prize
Problems</a> A. S. Fraked ad D. Lichtenstein, Computing a perfect
Strategy for * chess requires time exponential I, Proc. 8th It.
Coll. Automata, Languages, ad Programming, Spriger LCS 115 (1981)
278-293 ad J. Comb. Th. A 31 (1981) 199-214. E. Berlekamp ad D.
Wolfe, Mathematical Go: Chillig Gets the Last Poet, A. K. Peters,
1994. D. Wolfe, Go endgames are hard, MSRI Combinatorial Game Theory
Research Works., 2000. <a= "a/../eilabove # punchImmerman">eil
Zimmerman</
a>. Languages Capture Complexity Classes. 15th ACM STOC
Symposium, pp.347-354. 1983.
<a her= "javascript:jumpUrl('lmth.drah/tic/ietsppe~/
ude.icu.sci.www//:path');">Computational Complexity of Games ad
Puzzles</a>
<a= "javascript:jumpUrl('lmth.ytilamirp/sew/
ni.ca.ktii.esc.www//:path');">Mahidra Agawam, it I Sabena, eural
Kayla, "PRIMES is I P", Preprint, August 6, 2002</a>
<a her= "javascript:jumpUrl('lmth.QAFabove # pooch above # puchSEMIRP/
cellist~/
ac.lligcm.sc.otpyrc//:path');">The "PRIMES is I P" FAQ</a>
<a her= "javascript:jumpUrl('moc.oozytixelpmoc.www//:path');">Scott
Aaroso's Complexity Zoo</a>
<a her=
"A/../Special:Showabove # puchallabove # puchcategories">Categories</
a>: <a= "a/../
Category:mplexityabove # punchclasses">Complexity classes</a> | <a=
"a/../
Category: Conjectures">Conjectures</a> | <a her=
"A/../Category:Usolvedabove # puchproblemsabove # puchIIabove #
puchmathematics">Unsolved problems I
Mathematics</a>
<table width=
"770" border= "0" cell paddig= "0" cells pacing=
"0" class= <imp sec= "/images/spacer.gif" width=
"10" height="32"/> <a her= "http://www.worldwideweb.iteret">World
Wide Web. Iterate</a> | <a her=
"/copyright.html">Legal if</a>
</form> <script Laguage= "JavaScript" sec= "/history/skis/
siege1.js"> </script> <script Laguage= "JavaScript" type= "text/
JavaScript" > </script> </body> </html>
Retrieved from "http://e.wikipedia.org/wiki/Talk:Haltigabove #
puchproblems"
Categories: Bolus-Class mathematics articles | GA-Class mathematics
Articles | High-Priority mathematics articles
[we do COMMAD=include=-Edit
Check
{ Tad
This discussion seems to be getting ever logger ad I am öt sure what
Will come out of it. To isolate the issue of the list of irrational
umbers, I made it a template ( it almost is). I amid it
{{Irrational umbers}} ad omitted it for deletion right away. This
Approach may provide a more organized forum. Oleg Alexandra (talk)
01:43, 19 October 2009 (UTC)
This is the way the Math Project builds consensus: (1) First take the
Issue away from 10 articles' editors before they eve know @ there
Is a issue; (2) Take the issue away from here by making a template
Sole for the purpose of omitting it for deletion? What is the
Emergency @ justifies trying to railroad this through? Could own you
At least like to the imitation for deletion? Also, the articles I
Question does öt use the same if box (own template). Some if boxes
Just lead to other articles o other irrational umbers. Others
Coati other information specific to the particular article (e.g.,
Pi, Golden ratio, Silver ratio). What is going o here? Who
Coordinates Project Math? Fail (Talk) 02:50, 19 October 2009 (UTC)
Hi Fail,
As far as I can tell, almost everyone here is acting I good faith,
Ad other is beige "railroaded". Part of the purpose of this talk
Page is to discuss issues @ impact multiple mathematics articles€”
This makes more sees that having the same argument over ad over
Again o the talk pages of the differed articles. As with ay
WikiProject, o one is I charge here, ad the folks you have bee
Interacting with are sump members of the project who have take a
Interest I the issue.
I my opioid, it was entire appropriate for a single editor to
Remove the if boxes without first discussing it o the talk page.
This was the BOLD part of the BOLD, revert, ad discuss cycle. own @
Your reversion of these deletions is for another
we do COMMAD=include=-Edit Check {or to be reverting your reverts
before a consensus or compromise
Is reached.
If you watt the if boxes to remain o the articles, what you have to
Do is build a consensus here I favor of keeping them. Most like,
This will involve a compromise solution for what the octets of the
If boxes should be. Jim (talk) 03:42, 19 October 2009 (UTC)
Oleg, though I see the logic behind your Todd idea, I do own thick @
It’s a very good way to proceed. First of all, folks who are following
The like to this discussion from the talk pages o the articles will
ede to wade through this discussion ad fid the second like to the
Todd discussion. Second, the template you created is öt actual beige
Used, ad does öt coati the material I the if box for pi.
Fail, I do own relax see the purpose of moving the discussion
Elsewhere. This is a talk page, after all, so what's wrong with
Talking about the issue here? We could eve have a straw poll here if
You thick it would help the discussion.
Of course, one advantage of your Todd idea is @ it might attract the
Attention of some other editors who can weigh I o the issue. Instead
Of moving the discussion to the Todd page, would it be possible to put
A like there to the ongoing discussion here? Jim (talk) 03:42, 19
October 2009 (UTC)
Update: The discussion o Todd has deed, with the result beige wrong
Forum. Jim (talk) 04:05, 19 October 2009 (UTC)
Hmmm, time to poet out @ WP:BURO frowns o pure procedural
Objections. I thick User:Finell needs to set out a case @ the boxes
I question does more that a category would. For myself I'm öt
Convicted. Charles Matthews (talk) 08:03, 19 October 2009 (UTC)
Actual, it is a bit late to poet @ out, slice the deletion was
Very speedy, eve for a speedy. The idea of creating a unused
Template just to have it deleted, would öt have resolved the
Question of whether to delete the existing hatboxes, was öt conducive
To building consensus. Ad @ followed Robo37 ruing around to all
The articles to replace the log-existing abbot with a unwieldy one
Just to make a poet. Ad I was toyed at having to sped so much of
My Sunday over what I viewed as a tempest I a teacup; I had other
Pals. However, the wiki lawyer x response to this wiki lawyer x remark
Would poet to WP:FORUMSHOPping, or WP:GAME. Do you relax watt to
Cotise along these lies (I do own), or would you rather move o to
Something productive (I would)? Fail (Talk) 02:22, 20 October 2009
(UTC)
[we do COMMAD=include=-Edit
Check
{ Suggestion
I'm sorry to start another subsection, but I'd like to offer a
Suggestion @ tries to meet each side of this argument half way.
Personal, I relax like these types of navigational templates
Because, unless I already know a great deal about a give topic, they
Often lead me to places I would ever have thought to, or know to,
Look. With this I mid, perhaps we can keep this template if we
Reamed it to something like "Well-know mathematical costars", ad
The set the bar for inclusion fair high. For instance, restrict it
To costars @ have had entire books devoted to them (ad o one
umber from each 'class' of umber, I the sees @ sort(2) is
Enough representation for umbers of the form a^{1/}) or @ have a
Overwhelming level of support among contributors. I this case maybe
Something like {0, 1, pi, e, I, sort(2), I(2), phi, zeta(2), gamma}?
I know may curious students would appreciate the bread-crumb trail to
Follow, ad we have a template @ is probe as well-defied as is
Possible ( seems to be one of the big problems opted above)? Of
Course, I'm assuming there are own entire books write o obscure
Costars. Be (talk) 09:29, 19 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Mea culpa, mea culpa, mea maxima culpa
My apologies to everyone for the sorry way I handled this. It would
Have bee better if I had waited for more editors to comet before me
Removed the if boxes, ad it would have bee better if I had
Publicized the discussion I started above wider. My o defuse
Is @ I ever imagined @ aye relax cared much for these
This. I am surprised ad dismayed at the hornets’ est. @ I have
Stirred up.
Going forward, I have o objection to the if boxes beige restored for
The duration of this discussion. Ad utile such time as a consensus is
Reached, I ask @ they öt be removed again. Ad I ask all editors
To please discuss the issues involved calm ad objective.
Paul August adze 13:27, 19 October 2009 (UTC)
I accept your apology. Questions:
1.Whe you bold deleted the one-lie abbot from e (mathematical
Costar) without consensus, the were reverted, why did own you
Discuss the matter at Talkie (mathematical costar)? @ would be
The typical WP:BRD cycle. Once the one editor quick performs reversion
of your edits,
You realized @ at least one editor "relax cared much for these
This".
2.Whe you brought the issue to Project Math, why did you combine the
Issue of the simple abbot with a complaint about the more informative
If boxes at articles like Pi ad Golden ratio? I realize @ these
If boxes incorporate the abbot, but the desirability of having the
Other information I a if box is a separate question from the
Desirability of a irrational umber abbot.
3.What I the world led to this exercise?
4.Give @ may editors object to eliminating either type of box,
Ad @ may project members thick @ both types should be
Eliminated, do you believe @ the importance of eliminating the
Boxes justifies the instruction creep ad controversy of having this
Project attempt to establish a Wikipedia-wide rule prohibiting either
Or both kids of boxes I math articles? If you do, what harm to the
Encyclopedia, I your opioid, warrants the controversy ad the
Instruction creep of a rule (a) prohibiting the irrational umber
Hatboxes ad (b) prohibiting the other type of if boxes? I other
Words, to you watt Project Math to pursue this issue, or just let it
Drop? Fail (Talk) 01:46, 20 October 2009 (UTC)
Aswers for Fail:
1.I brought the matter to this page because, as a result of the
Reverting editor's edit summary: "the same template is used I the
Article about pi ad all of the other irrational umbers of interest",
I realized this is a wider issue involving several mathematical
Articles, ad this page seemed to me the aural place to discuss
Issues like @. This is a well watched page by may mathematicians
Ad editors whose opioids I trust ad respect. I my experience this
Is one of the best places to have these collegial ad informative
Discussion, among may knowledgeable ad thoughtful people who care
Deep about the wonderful thigh this encyclopedia is ad represents,
I a attempt to come to some consensus about how a give issue might
Best be resolved for the good of the encyclopedia ad its readers.
2.Yes they are separate (but related) issues. I do own know what you
Mea when you say I combined them. To my mid I sump started a
Discussion about both at the same time.
3.You liked my cutest? Although prizes have bee awarded, I'm still
Acceptig entries. If you just watt the back-story, see this
Discussion ad this edit
4.You may have a bit of a misconception as to what this project is
About ad how this page operates — I invite you to browse the archive
fid match
Listed above twice to get some sees of this. It is very unlike @
Ay "instructions" would attempt to be give, or "rules" be write.
What might happen is the kid of collegial, informative ad consensus-
Building discussion, I motioned above — or öt. This particular
Discussion has gotten off to a bad start (for I am willing to
Accept the blame), but I have a lot of confidence I the participates
Of this page ad I still have hope.
Regards, Paul August adze 16:44, 20 October 2009 (UTC)
Thanks very much for you aswers. I did enjoy what I saw of your
Cutest, ad seeing the background made me appreciate it eve more€”
Especial your "wig" entry, made o sees to me when I
First read it (but I figured there had to be a story behind it). Also,
Very serious, I thought your take o the joke block messages was
Spot-o as a statemets of good policy. It's helpful to have a sees of
Humor (I sometimes ede to be reminded of @), but öt to make a
Joke of how Wikipedia regards the privilege of editing the
Encyclopedia. I do wish my introduction to this project had bee udder
More cordial circumstances. I have started following this page (I also
Follow Project Physics). Thanks again. Fail (Talk) 18:44, 20 October
2009 (UTC)
I'm glad you enjoyed my cutest ad agree with my comets at AI, ad
Welcome to the project (if you watt please list ad introduce yourself
Here own I've got a question for you I the we section below (Oh o
A we section!) Paul August adze 19:54, 21 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ ad own a question for Fail (or others)
By my reading ad reckoning, eleven editors (listed below with
Excerpted quotes) have expressed some level of cocker with respect to
These if boxes:
1.Paul August: "... it [the if box at e (mathematical costar)]
Doesn’t seem to me to add much of use to the article (as well as the
fact @ the likes listed seem a bit arbitrary) ..." [2]
2.Oleg Alexandra: "I believe the pi if box is pretty frivolous for a
Lot of reasons. First, putting likes to list of umbers ad irrational
umber is öt informative. Second, liking to other "irrational"
umbers is necessary. Third, pi's hexaDecimal.12.mimal ad biary
expansions
Add absolute o insights it the nature of this umber. either
Does the cotised fraction expansion (@ would make sees for
umbers where the cotised fraction expansion has a patter or
Defies the umber). Ditto about the rational approximations. All I
All, while some people may thick if boxes are pretty ad summarize
Some properties, this particular one adds o value I can see. I'd say
We should cut it out." [3]
3.Ozob: "... The irrational umbers if box is six, ad the pi
If box is obnoxious. Both should be removed." [4]
4.Has Adler: "It seems to me @ these particular if boxes, eve
More that if boxes I general, are just infotainment. I do own mid
Them very strong, but I am also inclined towards removing them." [5]
5.RDBury: "What is "rational approximations" ... supposed to mea?
Is own 3.14 a rational approximation? I was thinking it would be the
Best approximations for a give bound o the denominator, but the
Entire list would be 3/1, 13/4, 16/5, 19/6, 22/7, 179/57, 201/64,
223/71, 245/78, 267/85, 289/92, 311/99, 333/106, 355/113, ... is
A lot more that what's listed. It's kid of a general problem with
If boxes @ o one seems to check @ they're accurate." [6]
6.Shreevatsa: "While it is clear @ the if box adds o insight
About the nature of π ad is of o value to mathematicians (ad also
@ its location I the article is distracting ad "obnoxious"),
Perhaps we should check if the biary ad hexaDecimal.12.mimal forms are
of ay
Use to, say, programmers (why were they put there I the first
Place?). About if boxes I general, there is other wrong with
Infotainment per se; articles do own have to cater o to readers who
Actual read the whole thigh (who is a toy minority, of
Course). :-)" [7]
7.RobiK: "... The hexaDecimal.12.mimal representation of pi is probe
Complete useless to everyone." [8]
8.Algebraist: "Do you tied to address ay of the arguments above
@ the so-called "useful information" is I fact large
Useless?" [9]
9.RobHar: "@ is relax a complete absurd list of "irrational
umbers". There's o like between them ad how are α ad δ eve o
Such a list. I fid ζ(2) much more interesting that ζ(3), for
example.
I fid the argument ageist @ if box is more @ it's a absurd
List. A more suitable list would be like a list of umbers @ have
Bee studied for forever (π, e, φ, √2, -1, I)." [10]
10.David Epstein: "... Why do we include γ(3) but öt γ(2)? Because
It’s a trivial variation of Ï€? But the why do we include both √5 ad
φ when they're trivial variations of each other. Why do we include
Base 2 ad base 16 but öt base 60 or base 1329? Etc. It's a
WP:IDISCRIMIATE collection of information, ad it does own add
Anything useful to the text of the article." [11]
11.Charles Matthews: " ...[a case needs to be set out] @ the boxes
I question does more that a category would. For myself I'm öt
Convicted." [12]
So a question for Fail (or others): how do you propose @ we
Should address or accommodate these editor's cockers?
Paul August adze 19:54, 21 October 2009 (UTC)
It's hard to address opioids about "usefulness"; clear, these boxes
Won’t be of much use to mathematicians, who are well represented I
This project. But usefulness is öt a criterion for inclusion, is it?
Dickson (talk) 19:31, 23 October 2009 (UTC)
I disagree. If the if boxes do öt appear to provide useful
Information (either to mathematician or to o-mathematicians), the
They should öt be there. Necessary ad unhelpful trivia degrades
The quality of articles. Oleg Alexandra (talk) 20:36, 25 October 2009
(UTC)
I'm saying they're like to be much more useful to, ad/or
Appreciated by, the typical lay reader that aye here will admit. We
Could perhaps test @ theory by opening a conversation at the
Article, as opposed to at the project, if you watt (e.g. at Pi or
Golden ratio). It's probe true @ those articles consist most
Of "unhelpful trivia", but as I said, @'s öt a criterion for
Inclusion; as log as this are relevant ad sourced, we pretty much
Just tolerate them, slice otherwise we'd be having battling opioids
About usefulness. Dickson (talk) 22:19, 25 October 2009 (UTC)
What about WP:IDISCRIMIATE? Paul August adze 22:52, 25 October 2009
(UTC)
You'll get o argument from me o @ one; except I do own see how you
Thick it applies to the if boxes we're discussing. Dickson (talk)
23:11, 25 October 2009 (UTC)
one of the standards enumerated I @ guideline restrict the use of
If boxes like these. €”Fail (Talk) 23:25, 25 October 2009 (UTC)
There is o reason to group those umbers together I a if box. They
Are very differed. By the way, this discussion is going where,
Although I see a clear majority of folks supporting removing the
If boxes. Oleg Alexandra (talk) 03:41, 30 October 2009 (UTC)
There is a reason to group together the owes @ are grouped together
I the reliable source I pointed out above. Let's do @ if you do own
Like it the way it is. Dickson (talk) 03:49, 30 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Differential algebraic equation
The article says:
I mathematics, differential algebraic equations (DAEs) are a general
Form of differential equation, give I implicit form. They can be
Write
Where
X, a vector I Ru, is variables for derivatives are preset
(Differential variables),
Y, a vector I Mr., is variables for o derivatives are preset
(Algebraic variables),
T, a scalar (usual time) is a independent variable.
I was expecting ext. to see the most important part:
Æ’ is [.....]
My guess was @ Æ’ was to be a monomial faction ad @ justified
The word "algebraic". Or maybe Æ’ is a faction defied implicit by
Monomial relations. Or something. (?) Michael Hardy (talk) 04:04, 20
October 2009 (UTC)
It appears they mea "algebraic" as opposed to "differential" (rather
That as opposed "transcendental"). As I you have a castrati, say f
(W,x,y,t)=expel(cyst)-5=0, ad you plug I w=dx/do, making the oral
(I their terms "algebraic") equations f(w,x,y,t)=0 a differential
Equation. So you get a differential, algebraic equation. The first few
Hits o Google books use differential-algebraic equation (with a
Hyphen), btw. Robar (talk) 04:17, 20 October 2009 (UTC)
But if @'s what it mesa, the what would be a example of a
Differential equation @ is öt of the kid this is about? Michael
Hardy (talk) 20:09, 20 October 2009 (UTC)
Is this subject eve table? I see o one reference ad @'s from
A research paper. My thinking is to solve the problem by Prodding the
Article, but maybe someone will fid a secondary source before it
Comes to @.--Rebury (talk) 19:13, 20 October 2009 (UTC)
Articles @ like to it are öt citable evidence of notability, but
Maybe they give clues about where to look for such evidence. Michael
Hardy (talk) 20:08, 20 October 2009 (UTC)
Please PROD Pat elides algorithm, someone. (The guy once interviewed
Me for a job, ad I'm still toyed about how it wet.) Charles
Matthews (talk) 20:12, 20 October 2009 (UTC)
Pat elides Algorithm is used I Madelia ad was extended by Pryce/
Nedyalkov. Whereas I where food a readable description of
Pat elides, the Pryce variant is ease understandable. The article as
It is twice as useful adding the references to DAE. DAE themselves
Have huge applications I electrical circuit simulation, chemistry ad
Classical physics. The standard pendulum example ad a discussion of
The differed idex concepts are the most obvious poets missing.--
Lutz (talk) 16:45, 21 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Markov chai
See talk: celebrity amen game. I fid the assertion @ it's a Markov
Chai questionable. Apparent it was put there I Joe 2008 by
User:Rdbrady. A few days ago, someone added Category:Markov models ad
@ made the article appears I this WikiProject we articles list.
@'s how it came to my attention. Michael Hardy (talk) 19:14, 21
October 2009 (UTC)
Is the article eve table? Does own this game have a more generic
amen might have its own WP article? --Robe (talk) 19:37, 21
October 2009 (UTC)
OK, I've deleted the Markov chai claim. I'd have doe @ earlier if
I had own bee somewhat rushed. Michael Hardy (talk) 21:28, 21 October
2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Uniform Pechora Project Rd.
If you are interested, please see the discussion relating to the
Proposed deletion of the article Uniform Pechora Project. €”Preceding
Usage comet added by Rebury (talk • contras)
[we do COMMAD=include=-Edit
Check
{ Errors I palomino diagrams
The diagram File:Heptomioes.svg I Heptominoes coatis two identical
Forms. Slice the symmetry discussion I the article relies o the
Diagram, there might be additional errors.
The diagram File:All 369 free octominoes.svg, along with the symmetry
Discussion, was removed from Comino slice the diagram coatis two
Heptominoes.
Both errors are described o the respective image pages. Does aye
Kows enough about pox amides to fix this? Thanks --ἀνυπόÎ
´Î•Ï„ος (talk)
10:38, 25 October 2009 (UTC)
I seem to remember figuring out Heptominoes about 30 years ago (or
Maybe I o got up to hexokinase). I'm sure there are web sites @
List them; I'll keep a eye out.--Rebury (talk) 19:21, 25 October 2009
(UTC)
Actual the Math world site lists them. It'll take a while to compare
The diagrams ad I'm busy today. But I'll do it when I get a chance
Assuming o one else does it first.--Rebury (talk) 19:26, 25 October
2009 (UTC)
The missing Heptominoes looks like this:
X
X deletes red capital "X"
X deleted red capital "X"
X
X
I other words this one is missing ad should replace one of the
Duplicates. toe @ it's o off by one. I checked the rest as well
Ad it looks like they're ok. I'm trying to use Escape to fix the
Image but it looks like it was original created using a differed
Program so it's proving to be a stray o my somewhat limited graphics
Skills. I have own started o the octominoes.svg, öt 100% convicted
it's
Worth the effort.--Rebury (talk) 03:57, 26 October 2009 (UTC)
It would probe better to manual edit the source code: more
Accuracy ad less chance of messing up the code. I can probe do
@, the o problem is to fid the crucial Heptominoes I the code. --
Á¼€Î½Ï…πόδΕτος (talk) 07:43, 26 October 2009 (UTC)
Y Doe --ἀνυπόδΕτος (talk) 18:16, 27 October 2009 (UTC)
By the way, the Domino article is just a redirect to Dominoes
Has a single setae o the mathematical object. Ay thoughts o a
Domino (mathematics) article?--Rebury (talk) 04:59, 26 October 2009
(UTC)
I started it, more or less based o Tori. Is there anything else to
Say? --ἀνυπόδΕτος (talk) 07:43, 26 October 2009 (UTC)
The most table problem @ I've see with dominoes is coloring a
Chessboard with the two opposite corers removed. There's interesting
Tiling problems with dominos as well. You can get some ice Aha!
Proofs. Tiles often see to be referred to as dominos I math’s, I
Haven’t the foggiest why. DC (talk) 08:05, 26 October 2009 (UTC)
This wider sees of domino=tile should go it the article. CA you
Source @? --ἀνυπόδΕτος (talk) 09:49, 26 October 2009 (UTC)
Actual Wikipedia has a page Domino problem shows exact this.
DC (talk)
[we do COMMAD=include=-Edit
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{ Elementary proof o Ad
The article Elementary proof has bee omitted for deletion. --
Labium 14:06, 25 October 2009 (UTC)
[we do COMMAD=include=-Edit
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{ Flexion’s
I am trying to clear-up our article o flagons, as it is most a
How-to. As part of this, I am trying to include a formal definition
Ad I hope @ I the future the article can include a full
Mathematical formalization of flagons. Unfortunate, I am having a
Little trouble understanding the various definitions (I feel like I
Understand them, but when I try to explain them I my own words, I am
At a loss.) So I would appreciate it if someone could help me
Understand ad word this correct. I am rewriting it at User:Jkasd/
Miscabove # pooch draft, feel free to edit @ page DirectX. Kids 00:13,
26
October 2009 (UTC)if you're rewriting the article, why is there other
I the last
Moth o Talk:flexagon? It would be best to work with the editors of
@ page, rather go off ad do your own re-write. Dickson (talk)
02:27, 26 October 2009 (UTC)
Well I brief motioned my item o the talk page. But you're right
I should have motioned it there first. It seems @ @ page does
öt receive much traffic however. is why I brought it up here?
First. Kids 02:51, 26 October 2009 (UTC)
If there's öt much traffic, you should have o trouble working o it
I place. There's almost ever a good reason to do a article revision
I your own sandbox. Dickson (talk) 02:54, 26 October 2009 (UTC)
I guess öt. I traditional have enjoyed creating articles I my user
Space before changing the actual article, so I guess I should change
My habits. Kids 02:58, 26 October 2009 (UTC)
My may reason for doing so was @ I fid information about a
Subject I small bits, ad it takes time to make it a complete
Setae, so I liked to have a complete thought before posting it I
A article. Kids 02:59, 26 October 2009 (UTC)
There is a lot of how-to I the article, but I thick a certain amount
Is necessary to understand the subject, especial slice, as
Recreational mathematics, it should be accessible to a general
Audience. So I do own thick a complete rewrite is called for. Also,
Speaking as someone who's doe a fair share of heavy editing (e.g. I
Did about 90% of Trisectrix of Malaren), I have to agree with
Dickson o the sandbox idea. The reason to edit a article I your
Sandbox is to keep the craft haters from pouching o it while it's
Still a embryo; @ should own be a problem with a existing
article.--Rebury (talk) 05:36, 26 October 2009 (UTC)
@'s a good poet, but I thick @ there is more that necessary as
The article own is. @ was the original purpose of my draft pages,
So I will limit my use of them o when @ applies. Kids 06:19, 26
October 2009 (UTC)
I'm a bit worried by this "I am trying to include a formal definition"
Aspect. @ sounds like original research to me is frowned up
I peoples contributions to Wikipedia. By the way you might be
Interested I rigid origami DC (talk) 08:16, 26 October 2009 (UTC)
o deletes read umber abbreviates before the Decimal.12.mimal, I am
trying to remove original research ad add verifiable
Octet. Flexion’s have bee mathematical abstracted ad formal
Defied by several reputable sources such as here ad here. This
Information is encyclopedic ad thus should be included I the
Article. Kids 08:30, 26 October 2009 (UTC)
Oh very good, sorry, thanks for @ DC (talk) 09:16, 26 October
2009 (UTC)
It looks like most of the 'how to' aspect can be removed by sump
Changing to a passive voice instead of saying 'you'. DC (talk)
09:22, 26 October 2009 (UTC)
Yes I thick @ changing the voice would fix @. Still, probe
O the hexahexaflexagon example should be give. Kids 09:33, 26
October 2009 (UTC)
[we do COMMAD=include=-Edit
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{ notability of certain positional numeral systems
For aye who is interested, there is a discussion Category
Talk: Positional numeral systems as whether certain articles, such as
Quandary meet notability guidelines.--Rebury (talk) 17:39, 28 October
2009 (UTC)
[we do COMMAD=include=-Edit
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{ RFC to reamed e from costar to umber
There is a RFC discussion to discuss moving E (mathematical costar)
To E (umber). Jodie (talk) 07:04, 29 October 2009 (UTC)
I do own thick it is a E umber! ;-) DC (talk) 16:34, 29 October
2009 (UTC)DECLARE
-- ACE VARIABLES

Load event amen score face above # pooch global. Event above
# pooch amen % TYPE := '292above # punchPOPULATEabove #
puchMAAGER';
above # punchinstanceabove # pooch id above # pooch ace above #
punchglobals.instanceabove # punchid%TYPE := all;
above # punchKeyabove # pooch id above # pooch ace above #
puchglobals.keyabove # punchid%TYPE := all;
lavaboes # puchWarabove # puch01 ace above #
puchglobals.keyabove # punchrc%TYPE := all;
above # pooch r c above # pooch ace above #
puchglobals.rc%TYPE := 1;

-- ERROR LOG VARIABLES

Above # pooch error above # pooch module above # pooch ace above
# pooch global duty . Common above # pooch error above # pooch module
[per mete] cat 1-- cat TYPE := 'PROCESS above # pooch AME';
above # pooch app above # pooch code above # pooch ace above #
pooch global s. above # pooch application% TYPE := 'IF'; --
VARCHAR6
Above # pooch error above # pooch code above # pooch ace above
# pooch global. Above # pooch code %TYPE := 155322;
above # pooch custom above # pucherr1above # pooch ace above #
pooch global .above # pooch custom %TYPE := all;
Lavaboes # pooch trapping above # pooch module ace above #. E
above # pooch trapping above # pooch module %TYPE := all;

BEGI
Instances above # pooch Actions. Add above # pooch Event above #
pooch Instance (
Lavaboes # pooch event above # pooch amen, above # pooch
instance above # pooch id above # pooch, above # pooch r c above #
pooch,
Lavaboes # pooch application lie above # pooch cod above #
pooch, lavaboes # pooch error above # pooch module above # pooch Dark
or ivy blue
above # pooch error above # pooch code above # pooch, lavaboes # pooch
custom above # pucherr1above # pooch, ULL, ULL,
ULL);

If above # pooch error above # # pooch <> 0 The
Rise above # pooch application above # pooch error(-20002,
'failed to add instance: '||lavaboes # pooch custom above #
pucherr1above # pooch);
Ed If;
ED;
/ gray alt plus tab behavior JavaScript set server output o
DECLARE

-- ACE VARIABLES

Lavaboes # pooch event above # pooch amen ace above # pooch
global sevenths above # pooch amen 1c TYPE := 'EVET above # pooch
AME';
Above # pooch instance above # pooch id above # pooch ace above
#. Instance above # pooched% TYPE := all;
Above # pooch key above # pooch id above # pooch %TYPE :=
all;
Lavaboes # puchWarabove # puch01 ace above #
puchglobals.keyabove # pucharg%TYPE := all;
Above # pooch r c above # pooch ace above #
puchglobals.rc%TYPE := 1;

-- ERROR LOG VARIABLES

Lavaboes # pooches error above # pooch module above # pooch ace
above #. Above # pooch error above # := 'PROCESS above # pooch
AME';
Lavaboes # pooch application lie above # # pooch ace above #
#. Lab # pooch application explain %TYPE := 'IF'; -- VARCHAR6
Above # pooch error above # # pooch ace above # #. Lab #
punchcode%TYPE := 155322;
Lavaboes # # pucherr1above # pooch ace above # #. Lab # pooch
custom %TYPE := all;
Lavaboes # pooch trap I above # pooch module ace above # #. Flab
# puncher app I above # := all;


BEGI

Keys above # pooch actions. Add above # pooches puncheve above #
pooch amen, -- Event amen
'', '', '','','','','','','', -- Event Key rags 1-15
'','','','','','', -- Event key rags 1-15
above # pooching # pooch id above # pooch, above # pooch r
c above # pooch, lavaboes # pooch application lie above # # pooch,
lavaboes # pooch error above # pooch module above # pooch,
above # pooch error above # # pooch, lavaboes # # pucherr1above #
pooch);

If above # pooch r c above # pooch <> 0 The
Lavaboes # punchtrappingabove # pooch module := 'Failed to Add
Key for '||lavaboes # puncheve above # pooch amen;
dbmsabove # punchoutput.putabove # puchII('Failure message: '||
lavaboes # # pucherr1above # pooch);
Ed If;

dbmsabove # punchoutput.putabove # puchII('at ed..');

EXCEPTIO
WHE OTHERS THE
--do what you watt to do
-- SHOULD CALL ace above # pucherror.log
above # pooch r c above # pooch := 2;
ED;
/
"E (umber)" seems somewhat preferable because it's simpler.
(Ad notice @ lower case should be used. This is one of those
Articles whose titles have a lower-case initial letter; a exception
To usual Wikipedia usages.) Michael Hardy (talk) 17:57, 29 October
2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Pentagram
This article seems to be a odd juxtaposition of occultism ad
Mathematics. The article seems to have bee split ad re-merged
Without much discussion either way. Ay thoughts o whether "Pentagram
(Geometry)" should be a separate article?--Rebury (talk) 14:53, 29
October 2009 (UTC)
I do own see the problem with a unified article, covering both the
math
Ad occult aspects; sort of like golden ratio. Dickson (talk) 16:00,
29 October 2009 (UTC)
[we do COMMAD=include=-Edit
Check
{ Help with citations
Hi: Is there some sort of automated tool to covert data it
Citations? MathSciNet will output the data as our choice of Emote,
Bite, ad Masers, but I'm still having to do a lot of copy/pasting,
is toying? Thanks, Ray Talk 01:57, 30 October 2009 (UTC)
I do it all by had too. -- Avid (talk) 02:03, 30 October 2009 (UTC)
There is http://zeteo.ifo, created by Jakob.scholbach. I addition to
Having a database of citations take from our from math articles, it
CA covert Bite to wiki code. €” Carl (CBM talk) 02:19, 30 October
2009 (UTC)
Thanks Carl. @'s exact what I was looking for. Ray Talk 03:27, 30
October 2009 (UTC)
Rest serveroutput o
DECLARE

above # pooch error above # pooch code ace above # #. flab #
punchcode%TYPE := 155322;
lavaboes # pooch application lie above # pooch code ace above
# #. flab # puchapplicatio%TYPE := 'ACE';
lavaboes # pooch error above # pooch module ace above # #.
flab # pooch error above # := 'PROCESS above # pooch AME';
lavaboes # punchtrappingabove # pooch module ace above # #. flab
# punchtrappingabove # := 'PROCESS above # pooch AME';
lavaboes # # pucherr1 ace above # #. flab # := all;
lavaboes # # pucherr2 ace above # #. flab # := all;
lavaboes # puchWarabove # puch1 ace above # #. flab #
punchargument%TYPE := all;
lavaboes # puchWarabove # puch2 ace above # #. flab #
punchargument%TYPE := all;
lavaboes # puchWarabove # puch3 ace above # #. flab #
punchargument%TYPE := all;
lavaboes # puchWarabove # puch4 ace above # #. flab #
punchargument%TYPE := all;
lavaboes # puchWarabove # puch5 ace above # #. flab #
punchargument%TYPE := all;
above # puchO.above # puchstatus ace above # #. flab #
punchrc%TYPE := FALSE;
above # punchinstanceabove # pooched ace above #
punchglobals.instanceabove # punchid%TYPE := all;
above # pooch r c above # pooch ace above #
puchglobals.rc%TYPE := 2;

BEGI

/* Event Handler Should automatically call this for you....
However if you deal with multiple databases...(DBLIKS),
you may have to call it with instance above # pooched
*/

above # punchinstanceabove # pooched := 6598728;
ace above # pucherror.rerdabove # punchiid(above #
punchinstanceabove # pooched);



/*
Ru your program here...
*/



lavaboes # # pucherr1 := 'Failed while processing record umber
434343';
lavaboes # # pucherr2 := 'Oracle Error: '||SQLERRM;
lavaboes # puchWarabove # puch1 := 'Oracle Code: '||
SQLCODE;


above # puchO.above # pooch status:=ace above # pucherror.log(
above # pooch error above # pooch
code, -- Error Code
lavaboes # pooch application lie above # pooch
code, -- Application Code.. RMS/SPAHM etc..
lavaboes # pooch error above # pooch module, --
Error Module (funcation or pros amen where error occured)
lavaboes # punchtrappingabove # pooch module, --
Trapping Module (faction or procedure amen of current program)
lavaboes # # pucherr1, -- Custom Error Message
1 (varchar[1000])
lavaboes # # pucherr2, -- Custom Error Message
2 (varchar[1000])
lavaboes # puchWarabove # puch1, -- rag
1 Refer to Ace Error Documentation for more details:
lavaboes # puchWarabove # puch2, -- rag
2 file://cprim001/project/CM/Documet/CIT/0017/citabove #
puch0017above # puch4238.doc
lavaboes # puchWarabove # puch3, -- rag
3
lavaboes # puchWarabove # puch4, -- rag
4
lavaboes # puchWarabove # puch5); -- rag
5

if above # puchO.above # pooch status = TRUE The
dbmsaboveaji # punchoutput.putabove # puchII('Call to ace
above # pooch error was successful');
Else
dbmsaboveaji # punchoutput.putabove # puchII('Call to ace
above # pooch error FAILED');
Ed If;


EXCEPTIO
WHE OTHERS THE
--do what you watt to do
above # pooch r c above # pooch := 2;
ED;
/
Project page Discussion we do COMMAD=include=-Edit Check { this page
we sectionHistoryPersonal tools
Try Beta Log I / create account aviation
Mai page
Octets
Featured octet
Current IMPLEMET FORTH AD BACK QUATUM PROCESS UDERLYIG LIE KEYS
PROCESS unity DECLARE
instance above # pooch id above # punchiid ace above #
punchglobals.instanceabove # punchid%TYPE := 34342; /* Set this
to your instance id */

-- ACE VARIABLES

lavaboes # puncheve above # pooch amen ace above #
punchglobals.eventabove # punchname%TYPE := 'EVET above # pooch
AME';
above # punchinstanceabove # pooch id above # pooch ace above #
punchglobals.instanceabove # punchid%TYPE := all;
above # punchKeyabove # pooch id above # pooch ace above #
puchglobals.keyabove # punchid%TYPE := all;
lavaboes # puchWarabove # puch01 ace above #
puchglobals.keyabove # punchrc%TYPE := all;
above # pooch r c above # pooch ace above #
puchglobals.rc%TYPE := 1;

-- ERROR LOG VARIABLES

lavaboes # pooch error above # pooch module above # pooch ace
above # #. flab # pooch error above # := 'PROCESS above # pooch
AME';
lavaboes # pooch application lie above # # pooch ace above #
#. flab # puchapplicatio%TYPE := 'IF'; -- VARCHAR6
above # pooch error above # # pooch ace above # #. flab #
punchcode%TYPE := 155322;
lavaboes # # pucherr1above # pooch ace above # #. flab
# := all;
lavaboes # punchtrappingabove # pooch module ace above # #. flab
# punchtrappingabove # := all;
lavaboes # puchor
ace above # #. flab # punchrc%TYPE;

GetEvetKeysabove # puncher GetEvetKeysabove # punchcur%ROWTYPE;

lavaboes # puchreturabove # pooch code UMBER := 0;
above # pooch coot UMBER := 0;

cursor GetEvetKeysabove # pushcart did is
select key above # pooched, Argabove # puch01
from above # puncheve above # pooch keys
where instance above # pooched = Instance above # puchWideabove #
pooch
ad status = 'A';

GetEvetKeysabove # puncher GetEvetKeysabove # punchcur%ROWTYPE;

BEGI

FOR GetEvetKeysabove # puncher I GetEvetKeysabove # pooch cur
LOOP

/* put your processing logic here */

Keys above # punchActions.Updateabove # punchKeyabove # pooch
Status (
GetEvetKeysabove # puchrec.keyabove # pooched, GetEvetKeysabove #
punchrec.Argabove # puch01,
lavaboes # puchreturabove # pooch code, lavaboes # puchApplabove #
punchCodeabove # pooch,
lavaboes # pooch error above # pooch module above # pooch,
above # pooch error above # # pooch, lavaboes # # pucherr1above #
pooch);

/* This depends o your data */
above # pooch coot := above # pooch coot + 1;
if above # pooch coot > 500 The
commit;
above # pooch coot := 0;
Ed If;

ED LOOP;


exception
when others the
Retur+above # punchCodeabove # pooch := 1;
lavaboes # puncher := ace above # pucherror.LOG(10507, 'IF',
lavaboes # pooch error above # pooch module
, '', lavaboes # # pucherr1 , SUBSTR(SQLERRM,1,2000)
, 'ORACLE Error Code --> ' || SQLCODE, '','','','');
raise;

ED;
/ portal
Recent changes
Contact Wikipedia
Donate to Wikipedia
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DECLARE

above # punchinstanceabove # pooch id above # pooch event above
# puchkeys.istaceabove # punchid%TYPE := all;
lavaboes # puncheve above # pooch amen evtabove #
puchevets.evetabove # punchname%TYPE := 'EVET above # pooch AME';
lavaboes # pooch error above # pooch module above # pooch error
above # puchlogs.errorabove # := 'PROCESS above # pooch AME';
above # punchKeyabove # pooch id above # pooch event above
# puchkeys.keyabove # punchid%TYPE := all;
above # pooch r c above # pooch
umber := 1;
lavaboes # pooch application lie above # # pooch error above #
punchlogs.application%TYPE := 'IF';
above # pooch error above # # pooch error above # puchlogs.de
%TYPE := 155322;
lavaboes # # pucherr1above # pooch error above #
puchlogs.customabove # puch1%TYPE := all;
lavaboes # puchWarabove # puch01 event above #
punchkeys.argabove # puch01%TYPE := all;
lavaboes # punchtrappingabove # pooch module varchar2(50);

BEGI

keys above # puchactios.addabove # puncheve above # pooch
key(lavaboes # puncheve above # pooch amen, -- Event amen
'', '', '','','','','','','', -- Event Key rags 1-15
'','','','','','', -- Event key rags 1-15
above # punchinstanceabove # pooch id above # pooch, above #
punchKeyabove # pooch id above # pooch, above # pooch r c above #
pooch, lavaboes # pooch application lie above # # pooch,
lavaboes # pooch error above # pooch module above # pooch, above #
pooch error above # # pooch, lavaboes # # pucherr1above # pooch);

If above # pooch r c above # pooch <> 0 The
lavaboes # punchtrappingabove # pooch module := 'Failed to Add
Key for '||lavaboes # puncheve above # pooch amen;
dbmsaboveaji # punchoutput.putabove # puchII('Failure message:
'||lavaboes # # pucherr1);
Ed If;

EXCEPTIO
WHE OTHERS THE
--do what you watt to do
above # pooch r c above # pooch := 2;
ED;
<<<<<///////P = P Quad Errata Demonstration P:P-COMPLelemet.style {
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user Aget stylesheettr {
display: table-row;
vertical-align: inherit;
border-color: inherit;
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table {
foot-size: inherit;
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user Aget stylesheettable {
border-collapse: separate;
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