P=NP___Authors: Selmer Bringsjord, Joshua Taylor
"To develop the skill of correct thinking is in the first place to learn what you have to disregard. In order to go on, you have to know what to leave out; this is the essence of effective thinking." Kurt Godel
"Time and space are modes in which we think and not conditions in which we live." Albert Einstein
Since the days of Socrates, Plato and Aristotle, there has been a division of thought pertaining to arithmatic, logic and truth, as to which is prime. I intend to show beyond doubt that arithmatic is prime. I will do this with 18 maximal triadic thought statements. The statements only apply to the ultimate ability of thought to reason thoroughly open and independently of strict rational thought, though they can apply in many other areas of thought. That is not my itention. I’m dealing only with the sources of ancient and modern thought problems. I’ll start this off with a few general universal axioms:
"A priori arithmetic is the greatest philosophy knowable to humanity." me
“There exists no mind or machine, sufficiently powerful, to process finity and infinity, simultaneously!”___Proofs below…
“The highest probability, of the highest possibility, is the only possibility.”
Now, I’ll list 6 triadic axioms of math, truth and necessity:
1.The highest probable truth, of the highest possible math, is the highest necessity possible.
2.The highest probable truth, of the highest possible necessity, is the highest math possible.
3.The highest probable math, of the highest possible truth, is the highest necessity possible.
4.The highest probable necessity, of the highest possible truth, is the highest math possible.
5.The highest probable math, of the highest possible necessity, is the highest truth possible. ***
6. The highest probable necessity, of the highest possible math, is the highest truth possible. ***
So far, so good, these are all true, with #5 and #6 being highest truths possible. Next I’ll list 6 more triadic axioms of logic, truth and necessity.
1. The highest probable logic, of the highest possible truth, is the highest necessity possible.
2. The highest probable logic, of the highest possible necessity, is the highest truth possible. ***
3. The highest probable truth, of the highest possible logic, is the highest necessity possible.
4. The highest probable truth, of the highest possible necessity, is the highest logic possible.
5. The highest probable necessity, of the highest possible logic, is the highest truth possible. ***
6. The highest probable necessity, of the highest possible truth, is the highest logic possible.
Again, so far, so good, these are all true, with #2 and #6 being highest truths possible. Next I’ll list 6 more triadic axioms of math, truth and logic.
1. The highest probable math, of the highest possible truth, is the highest logic possible.
2. The highest probable truth, of the highest possible math, is the highest logic possible.
3. The highest probable logic, of the highest possible math, is the highest truth possible. ***
4. The highest probable math, of the highest possible logic, is the highest truth possible. ***
5. The highest probable logic, of the highest possible truth, is the highest/lowest math impossible. --- i.e., infinity and infinitesimal at the absolutes ---
6. The highest probable truth, of the highest possible logic, is the highest/lowest math impossible. --- i.e., infinity and infinitesimal at the absolutes ---
Finally, we arrive at the ultimate incompletenesses of both math and logic. While four of the above axioms are true, and #3 and #4 are of highest truths possible___there exists no math to process axioms #5 and #6. This has grave meaning for the history of logic. The sets of [truth and logic],[logic and truth] entail math impossibilities, under any rational or irrational math systems, that rationally connect infinity and finity. The math can’t go___and the logic can’t prove___The ultimate truths are P=NP Incomplete. The universe can’t wholly be described without a completed infinity/infinitesimal math and logic integration, thus this proves the incompleteness of math, truth and logic, at the abosolute___As logic ain’t logic without math___Logic less math ain’t logic___It’s Foo-Foo-Land!
At first, logic seems to entail more power than math, yet itself entails ego-omniscience, irrationality and incompleteness, making itself useless alone, as Naked Logic. Naked logic is quite a Trickster, though... Yet, even if I represent infinite and infinitesimal math with symbols X/X=1+IEE(isomorphic extension entanglement), and X/-X=1+IEE(X=finity, or infinity, or infinitesimal as applies), there’s no way for me to connect these formulas rationally to finity, with either isomorphic mappings or any sensible forms of other group, etc., maths, therefore it spells the death nell for Aristotle, Hegel, Frege’s, Russell’s and all analytic philosophy, trying to use S5 modal logics, and other logics and truths, to prove linguistics, semantics, propositions, syntax or whatever. Oh, they may create many more algorithms to improve computer software and robotics operations, but they’ll never achieve their dreamed of AI, as this incompleteness makes it impossible, unless future math can some day bridge the true and absolute infinity/infinitesimal gap, as logic and math separate, at the absolute origin, thus are separate agents within our a priori essense agency. Arithmatic is the only true and prime a priori epistemic agent, when comparing math and logic. Logic is a tool of our epistemic agency, yet the math agent is deeply ingrained within the primary epistemic agent of perception. Why wouldn’t it be, it demensionalizes and geometrizes all our images, even in primary passive visual inductions of.
Peirce tried to warn them all over a hundred years ago, but the world wouldn’t listen. Even after Peirce’s warnings, Frege, Russell, Wittgenstein, Carnap, Tarski, Quine and the likes of Chomsky kept marching down this false road of no sensible end. On the other hand, Huygens, Jevons, DeMorgan, Gibbs, Schroder, Peirce, Veblen, Einstein, Keynes, Paul Davidson and others, took the correct path of Always attaching Arithmatic/Math to Logic, to make real world sense. Too bad___Just the way it is…
P=NP Incomplete holds, and arithmatic precedes logic, not only by the above evidence, but by the fact there could never have been any logic in the early universe, as it’s a non-living mass of matter and motion, guided simply by random and chance actions on matter. Ain’t got no human logic, just the combinatoric arithmetic of basic fundamental substance forming first Bose/Einstein condensates, into much, much later galaxies, solar systems and planets with moons, etc, etc, etc…
29 comments:
Dear Marcus Aurelius,
I am writing to thank you for your valuable contribution to mathematics and logic. Your comments are well thought out and commanding. My one criticism is that we must always remember the difference between symbolic logic and real logic. In Quantum Computing we throw worlds around like infinite and infinitesimal and then conclude on the basis of the positioning and ordering of the letters we choose to represent them. I caution against absolute absolutes though I love the commitment to base design in oppositition to what some would claim. Indeed we are not simply beings swarming around a cosmic hive. There is an order to these things and that order is life. http://pversusnp.wordpress.com
Martin Michael Musatov
The Original Prover [P=NP] Moreover [Musatov = EZZ (complexity)]. (for now) "I may be the first but I am not the last and there are certainly others who came before me."
My final comment to mark this momentous occasion is it has only begun!
-----------------------------------
A Message About Egpyt46 This is the word of the Lord to the prophet concerning the nations:
2Concerning Egypt:
This is the message against the army of Pharaoh Neco king of Egypt, which was defeated at Carchemish on the Euphrates River by Nebuchadnezzar king of Babylon in the fourth year of Johoiakim son of Josiah king of Judah:
3"Prepare your shields, both large and small,
and march out for battle!
4Harness the horses,
mount the steeds!
Take your positions
with helmets on!
Polish your spears,
put on your armor!
5What do I see?
They are terrified,
they are retreating,
their warriors are defeated.
They flee in haste
without looking back,
and there is terror on every side," declares the Lord.
Thanks for the comments, Martin. I liked your quote: "If smart people always had Ph.D.'s we would not have light bulbs."
P=NP___What's the computation algorithm for the aggregate web of computers...?
For now if you want to pay me we can speak. If you do not get behind me.
The absolute arithmetic, of absolute pure knowledge, is the absolute law of pure liberty, which holds the absolute wisdom. The absolute law of pure liberty is isomorphic to the extremal ends of the conservation law of matter/energy, fields/motions, under the physics of absolute ground state hydrodynamics.
The above contains the seed of the isomorphic laws of the geometry of the universe and the true computations, of computations, of P=NP complete.
I'll be publishing shortly on the absolute trans-finite explanations, of arithmetic childhood perception and imagination mechanics.
The Triadic Maxim___Any idea; "Arithmetically check all possible effects, against all possible premises, and the combined results will be the total actions of the idea".
BTW, absolutes are absolutely necessary to fully explain, even the finite `quantifier logic' uses, and extended physical logical actions...
Hey Paul Krugman___A Song___A Plea
http://www.youtube.com/watch?v=XOYAuk809fY&feature=PlayList&p=C9531633DA225E44&index=0
Gödel admits P=NP
Yeah P=NP possible, but not yet...
Requires universal isomorphic quantification logic___Kant, Frege, and Peirce, also Pythagoras, Archimedes and Einstein___The super-triads of universal semantic/pragmatic logic...
P=NP, the Answer Is Truth
A definitive proof of decidability and Truth, plus numerical formulation and computational proof of Polynomial Time Achieving
by Martin M. Musatov, 9 January, 2009.
There has been much debate surrounding answers to the question of P=NP.
A defeatist attitude with limited scope of imagination or lack of creative intellect may labor over a simple Catch-22; namely claiming that the problem is we cannot answer the question until we have successfully asked the question, and then asserting the question is impossible to ask, therefore it will never be answered.
I will first demonstrate this behavior and thought pattern is the equivalent of staring out a window and thinking you cannot walk through it because you see your reflection in it.
Consider this statement as my response to this very point, it is, it is in fact, evident, as I, as "P", hold it in queue with words, that all statements are answers to some question, independent of whether or not the question has been asked. In fact, later the question could be asked, did he spend a great deal laboring this point, and in fact I did, thereby answering question, yes, I did. Though I did not know the question was to be asked, I factored the possibility, assuming the condition occurs does not mean its consideration caused it to occur when it does.
Further, consider the formulation of the possible outcomes to my attempt to disprove un-decidability of P=NP. Though I am writing about it right now, and factoring information about these outcomes, and hoping not annoying you by belaboring this point, this process is independent to the possible outcomes or the aim by which you will later chose to formulate or anticipate responses to those questions, that have not been skewed and specifically, let's factor them right now:
But, before we get into that--record screech--- (Halting problem)--Re-Re-Re-Regardless as if you are imagining me as Max Headroom right now, or if I am aiming to prove or disprove P=NP, or some asymptomatic condition precedent in my success, you know I am thinking about it; to successfully formulate any proof to P=NP is the same to the algorithm, straight forward, but only if the right approach.
Consider the possible outcomes of my attempted proof or disproof; factor them:
A) I will sufficiently prove falsehood of un-decidability, with respect to its claim.
B) Succeed in proving P=NP is true.
C) Fail.
In any case, there are three possible outcomes to which I acknowledge to differentiate completeness, however if "C" occurs it is impossible A and B occur. Therefore any claim of simple un-decidability, on a true/false of even simple Boolean logic is based on a single formulation by which to communication one way to present A or B only, and no dependents is disproven as legitimate to claim any factor of un-decidability. Explicitly, because there are endless formulations or combinations of questions by which to ask in varied sequence which would satisfy an infinite number of words and letters in which to choose to convert them, thereby proving definitive the condition definitively as false or proof.
But you might be asking, what did you last mean by proof? In what sense were you asking? By what means did you ask the question would be my response in polynomial time if I were an algorithm. But either way, you can assume, since I am a machine, I am factoring all know possible logic conditions by which are know to my input way by which to later present it, given your command to do so.
A denial, and yet still this formulates a statement of truth, pending. It is this type of logic, which guides the underlying theorem of P=NP. For any statement of un-decidability therefore, I will drill holes the size of Texas, (or at least the size of P). Consider, as I am keeping polynomial real-time in this writing, as if I am sitting next to you talking or you are reading these words as I type them. This is the essence of Polynomial Time. Since it never stops, it never stops is always one factor ahead of you based on information it has factored prior to it, next response:
1) A provable answer to the question P=NP requires a complete and consistent formal statement of the question.
Rationale: Hopefully, this is self-evident. It is certainly axiomatic that a formally provable statement be expressed in formal terms. Completion and Consistency follow from the requirement to provide a proof that is not subject to challenge.
2) A complete and consistent formal statement of the question must incorporate a complete and consistent formal definition of the sets P and NP
Rationale: Hopefully, this is also self-evident. (I have left out the requirement to define the equality operator, since it is defined for us by set theory.)
3) A definition based on a potentially detectable characteristic is complete.
Rationale: We can accept the definition of the set NP purely in terms of its members having a property (a solution test in polynomial time) that we have a reliable mechanism to detect. Therefore, a complete definition of the set NP will be arrived at via these means.
4) The only possibility for a complete definition of the set NP is a language.
Rationale: Once we rule out observation of characteristics, our only means towards a definition of the set NP is to formulate a language, a procedure for testing the formal expression of the candidate problem that will accept the problem or reject it.
5) No formal language capable of expressing non-trivial mathematical problems can be infinite and complete. However given Einstein's establishment of relativity and the spacetime curvature a consistent stability is reachable if contained by proactive measures.
Rationale: As proven by Gödel.
6) Therefore, a consistent and complete definition of the set NP is possible.
Rationale: If we accept that the set NP can only be rigorously defined via a language, this conclusion follows from the premises above.
7) Therefore, a consistent and complete statement of the problem of P=NP is possible.
Comment: A conclusion which is not only proven in this paper, but supported by the years of argument between mathematicians regarding the relevance of proposed answers to the problem.
8) Therefore, P=NP is decidable if physics and causality is rationale.
Comment: Given our inability to make this statement, we are able to answer the question.
Conclusion: Since stability of mass is obtained by variable assignments which are arbitrarily defined by symbolic systems such as languages and increased modalities of accuracy, we consciously subdue unknowns in an effort to excel. We acknowledge every statement made can be interpreted to be a question and every answer made answers a question whether or not the question has been formally proven. Given this case, P==NP is no longer an eventuality, it is therefore a certainty.
--Martin Michael Musatov
I should have informed you, I have prepared a much stronger version of the Selmer Bringsjord, Joshua Taylor paper to which I am "Interlocutor". In fact, I would like to publicly offer you the below information as proof of this fact: Here is the compiled file as was used in its preparation:
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For your publishing convenience, I have uploaded the .pdf to share with you here: http://www.scribd.com/doc/13690179/Salt-Light.
Please augment these results, solidify these efforts, and proceed to publish them. I simply ask to maintain credit as "interlocutor".
Sincerely in Trust,
--Martin Michael Musatov
I have recently launched a new blog, search engine built on Google's API, and a Wiki-like platform called WikiWikiWeb built on PHPWiki.
I would like to share them with you and encourage you to make use of the search in your physics and computational complexity work.
The search engine is at:
"http://www.MeAmI.org/The blog is at "http://MeAmI.org/blog/.
And the WikiWikiWeb is "http://MeAmI.org/wiki/.
I wish you all the best in your endeavors and salute your research and tolerance of my temperament. --MMM, m[dot]mm[at]vzw[dot]blackberry[dot]net.
To fix those quotes:
http://MeAmI.orghttp://MeAmI.org/bloghttp://MeAmI.org/wiki
You having fun? So far you haven't sent the correct web links. I have all the ones so far sent...
As to languages and formulations, the language of questions must be finite arithmetic, where the proper question is; "What is the true fundamental mathematical problem with capitalism? Or any other form of heiarchical organization, of any other possible non-destructive social contracts?"
P=NP i.e., Proof=NonPossibles, add em up, and choose what's left___the possibles...
It's just a simple combinatoric process, existing from the earliest of written and recorded languages...
All conversions of unknowns are achieved by isomorphically changing/updating psychologies/semantics to arithmetic logics through their global pragmatic uses...
Shtetl-Optimized Blog Archive Popular complexity9 Feb 2009 ... Note: As of February 20th, 2009, a proper binary solution to the P=NP problem was formulated by Martin M. Musatov. ...scottaaronson.com/blog/?p=385 Is this th correct web link?
Shtetl-Optimized Blog Archive Popular complexity9 Feb 2009 ... Note: As of February 20th, 2009, a proper binary solution to the P=NP problem was formulated by Martin M. Musatov. ..http://.scottaaronson.com/blog/?p=385 Is this th correct web link? Oops...
Shtetl-Optimized Blog Archive Popular complexity9 Feb 2009 ... Note: As of February 20th, 2009, a proper binary solution to the P=NP problem was formulated by Martin M. Musatov. ..Is this th correct web link?
A True Triadic Linguistics___Words; Logic; Numbers___The Natural Whole...
Key___True logic(logical truth) only functions quantificationally through math...
I agree. That is why I am glad it was proven 6P=NP back in 1965. Those were the day, eh Lloyd?
--Musatov
So indeed Mr. Musatov (triadic 3rd POV): has proven P=NP against the problem. A single revision suggests: "All statements and even questions may be interpreted as answers whether or not the question [emphasis]:"could" have been asked. We do not need physical bounds of a rational universe in this definition of "proof" as logic through math tells us any number may be computed and perceived as the answer to an infinite question. Therefore we cannot ask: for example, consider this proof: GooglePlex!(Factorial)^Googleplex/Googleplex (Factorial)=Googleplex^Googleplex. As we may never have the time or memory to confirm the results or compute the answer we can acknowledge the possibility of asking and answering the question correctly. Even if the answer is incorrect all still required is established for this "Musatov's proof P=NP".
The Awakening of The American Mind: P=NP Incomplete___The Maximal ... 1) A provable answer to the question P=NP requires a complete and ... MeAmI.org/ The blog is at "http://MeAmI.org/blog/. ... theawakeningoftheamericamind.blogsp...
The Awakening of The American Mind: P=NP Incomplete___The Maximal ... 1) A provable answer to the question P=NP requires a complete and ... MeAmI.org/ The blog is at "http://MeAmI.org/blog/. ... theawakeningoftheamericamind.blogsp...
"All statements and even questions may be interpreted as answers whether or not the question [emphasis]:"could" have been asked. We do not need physical bounds of a rational universe in this definition of "proof" as logic through math tells us any number may be computed and perceived as the answer to an infinite question. Therefore we cannot ask: P=NP".
Ahhhhh...I finally see where you are at___You are wrong...!
Anytime you consider a singularity, i.e., math or logic, you make the mistake of not considering the Triadic Maxim, Any Idea___"Arithmetically check all possible effects, against all possible premeses, and the combined results, will be the total actions, of the idea." You cannot figure P=NP complete, without the completed triadic idea, i.e., EFFECTS; PREMISES; RESULTS...!
I suggest you study Charles Sanders Peirce. You may then realise, there is a completion algorithm to the elimination of un-necessary power, which must be premised triadically, tria-chronically; PAST; PRESENT; FUTURE, or WAS; IS; OUGHT. Then, you may realize there are real arithmetic solutions to the power paradigm...
Clue___The power paradigm must be separated into its power distinctions___The Triadic Distinctions, i.e., "Logica Utens", "Logica Docens" and "The Real World of Triadic Powers". Also the "Moral/Ethical/Un-Ethical" Distinctions. Also the "The Triadic Logic" Distinctions, Intuition; Logic; Math, and Logic's own triadic content, "True; False; Possible", "Isomorphic; Non-Effective; Effective".
You seem to be forgetting we live in a real world of "People's Habits" and "Effectable Possible Changes." That takes "Intuition" applied over "Logic" and "Math", then Math applied over and transducted back, around and through the logic and intuitions, i.e., senses___The sensible "Better Nature" senses, over the "Higher Nature" senses...
BTW, all necessary algorithms can be formulated to answer all and any "VALID" question, to solve the massive world problems...
Hint; The Greek's Triadic Intuitions, Maths and logics, from Pythagoras to Arhimedes. Forget Aristotle's nefarious separation silly-gistic logics, they're invalid, all the way to Frege/Quine, even though Quine does offer the "Distinctions", his "Minor Logic" must be implanted inside Peirce's "Major Pragmatic Quantification Logics"...
The Greek's just lacked the "Mean Terms" of "Isomorphic Understandings". Peirce filled that in, when re-adopting their "Triadic Systems"...
Best Clue; All Quantifiers are Infinites, over Finites...
Think about it...
Math/Logic hasn't learned this___Yet...!
Okay, well let's get into it. What do people do? Universally they search for things in every culture, every logic, every kingdom, every race, since the beginning of time:
A Search for a result:
Limning Omniscience - The ProsblogionBut, lastly, let's suppose there are no actual infinites. ... So, all there is to know is summed up in some finite number of actually true propositions. ... (Actually, there would be no problem in quantifying over the set of all sets of ... I'm rejecting the interpretation of the English quantifier in "God knows ...http://prosblogion.ektopos.com/archives/2008/12/grimful-omnisci.html
Emerald FullText Article : Modern system of mathematics and a pair ...is identical to “for all x … ”. The symbol ∀ for the quantifier came .... over N. Then, the variable k can increase and approach ω without bound. Since, in mathematics, it is assumed that the magnitude of each natural number is finite, .... infinites, beautiful and not beautiful, good and not good, etc. are all ...http://www.emeraldinsight.com/Insight/viewContentItem.do%3FcontentType%3DArticle%26hdAction%3Dlnkhtml%26contentId%3D1722938%26dType%3DSUB%26history%3Dfalse - 3rd: Alain Badiou – Logic Course (1982 – 83) « Stellar Cartographies9 Jul 2008 ... ß is closed by the universal quantifier (≠ existential closure) ... the predicates to the themselves, holding quantifications over properties. ... theories categorical for all infinites separately; ex. theory of vectorial spaces ... (Uncreated) God was infinite and the (created) world was finite. ...http://stellarcartographies.wordpress.com/2008/07/09/3rd-alain-badiou-logic-course-1982-83/ Ch.1 (Part 3): The Foundations: Logic and Proof, Sets, and FunctionsSequences, Summation, Cardinality of Infinites Sets (1.7). The set of (finite length) strings S over a finite alphabet A is countably infinite. ...http://djamel-bouchaffra.info/discretemath/504ch1part3.ppt Quantifier elimination, valuation property and preparation theorem ...An infinitesimal µ is active over a finite set λ ...... We are now in a position to prove a basic theorem on an active infinites-. imal, stated below. ...http://www.maths.manchester.ac.uk/raag/preprints/0239.ps.gz Ephilosopher: Forums / Philosophy of Science Forum / Is classic ...It would have been true if they neglect the "all' quantifier, .... finite groups, the brain implies this order to the large and infinites groups of objects. ...http://www.ephilosopher.com/e107_plugins/forum/forum_viewtopic.php%3F57948.10 [FOM] Size theory.And the addition, multiplication and exponentiation rules of algebra of finites will be applicable on Z. More over we have 2Z > Z+w were w refers to w While ...http://www.cs.nyu.edu/pipermail/fom/2008-April/012806.html Gunnel Kallgren Institutionen for lingvistik Stockho]ms ...The analyzing programs are all based on pattern matching procedures on different ... clause p = prepositional phrase d = determiner q = quantifier e = preposition r ... infinite verb v = finite verb j = adjective w - finite verb or noun k .... Possible infinites are unmarked words with one of three possible surface ...http://www.sics.se/nlp/NoDaLiDa/1983_ups/NODA83-16/NODA83-16.txt NONSTANDARD MATHEMATICS Pisa, Italy May 2006 ERNA + TRANSFER Sam ...Free-variable axiomatic foundations of infinites- ... finite procedure. Hence: quantifier-free (sometimes artificial look- ing) axioms. ...http://www.dm.unipi.it/~nsm2006/slides/sanders-s.pdf Representation of Modal Intervals within a Computer - Patent ...The modal interval representation generally includes a binary quantifier, ... Such representations do not specify semantics for all possible bit-patterns of ...?
P=NP+Complete.
And...What's the point? You still haven't laid out any real world mathematics. Just propositions, that may or may not be true. I don't try to do math on non-sense.
One must start from real applied arithmetic premises, first. Like logically true global system(s) functions, to first quantify over...
Know what I mean...?
There's no since starting deep inside the system, where truth's impossible to quantify...
Peirce's graph assertions start from the outside and go in, not the reverse. Inductive logics and maths, first...
KISS, and stop splashing ink...
My new post:
http://theawakeningoftheamericamind.blogspot.com/2009/05/history-of-historyeclecticismwhere-is.html
comp.theory | keyongtechGo to first new post I Just Proved [P=NP] and I get to announce it on Usenet. Martin Michael Musatov. 04-29-09 08:35 AM by Jesse F. Hughes ...="http://www.keyongtech.com/comp-theory/" - 30k - Cached - Similar pagesLloyd Gillespie (PiLogic) on Twitter... P=NP___What's the computation algorithm for the aggregate web of computers...?11:09 AM Apr 23rd from web; P=NP. Professor Martin Michael Musatov. ..."http://twitter.com/PiLogic" - 38k - Cached - Similar pagesUser:MartinMMusatov page on SklogWiki - a wiki for statistical ...P = [■(&⋯&@⋮&⋱&⋮@&⋯&)] N (■(&⋯&@⋮&⋱&⋮@&⋯&)) P. [[P=NP]through Parallel Tempering --MartinMMusatov 01:11, 24 February 2009 (CET)Martin M. Musatov ..."http://147.96.5.37/SklogWiki/index.php/User:MartinMMusatov" - 14k - Cached - Similar pages
If I am going to prove P=NP it is going to be against you. You are one smart cookie.
Could it have to do with the trinity(In the broadest)? Making change? (At a store)
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