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Topic: Counting argument

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	Double counting - Wikipedia, the free encyclopedia
		In combinatorics, double counting, also called two-way counting, is a proof technique that involves counting the size of a set in two ways in order to show that the two resulting expressions for the size of the set are equal.
		Double counting is also a fallacy in which, when counting events or occurrences in probability or in other areas, a solution counts events two or more times, resulting in an erroneous number of events or occurrences which is higher than the true result.
		Once the principles of the value theory are established, categories and counting units can be exactly and logically defined, as a basis for mathematical operations to aggregate the flows of incomes and expenditures.
	en.wikipedia.org /wiki/Double_counting (1461 words)

	Combinatorial proof - Wikipedia, the free encyclopedia
		A combinatorial proof is a method of proving a statement, usually a combinatorics identity, by counting some carefully chosen object in different ways to obtain different expressions in the statement (see also double counting).
		Since those expressions count the same object, they must be equal to each other and thus the statement is established.
		A statement is said to be proven combinatorially if a combinatorial argument, or counting argument, is used in the aforementioned fashion to justify the key steps of its proof.
	en.wikipedia.org /wiki/Combinatorial_proof (401 words)

	Profile of
		Counting both stones and spaces as territory is a precondition for determining life and death by removal.
		The fill-in counting procedure is as follows: (1) At the end of the game, both players fill all prisoners, dead stones, and the stones remaining in their bowls into territory of the same color.
		The traditional Chinese counting system did not distinguish between stones and spaces, but required every group to have two breathing points which were not counted as territory, creating in effect a tax on groups: the player with more groups had to give up one stone for every excess group.
	www-2.cs.cmu.edu /~wjh/go/rules/SST.html (11130 words)

	Counting Argument Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-26)
		Enumerative combinatorics came to prominence because counting configurations is essential to elementary probability, starting with the work of Pascal and others.
		Two of the most prominent combinatorialists of recent times were the prolific problem-raiser and problem-solver Paul Erdős, who worked mainly on extremal questions, and Gian-Carlo Rota, who helped to formalize the subject beginning in the 1960s, mostly in enumeration and algebraization.
		However, given that we are looking at a counting function, the presence of the √5 in the result may be considered unaesthetic.
	www.artisticnudity.com /encyclopedia/Counting_argument (1615 words)

	[No title]
		(count factors of 3 mod 8 -- observe that 3*3 = 1 mod 8).
		We need to count the number of these which turn out to be "negative": it is easy to see (because 2*P = p-1 < p) that the "negative" ones are exactly those that belong to residue classes greater than P computed in the usual way.
		The argument that the product of two non-squares must be a square is a counting argument -- let q be a non-square -- multiplication by half of the non-zero residues (the squares) yields non-squares, so multiplication by the other half(the non-squares) must yield squares.
	math.boisestate.edu /~holmes/holmes/cryptofiles/Notes2.txt (2106 words)

	TomPaine.com - Kerry Won. . .
		Today, the Cleveland Plain Dealer reports there are a total of 247,672 votes not counted in Ohio, if you add the 92,672 discarded votes plus the 155,000 provisional ballots.
		Count them up, add in the spoiled punch cards (easy to tally with the human eye in a recount), and the totals begin to match the exit polls; and, golly, you've got yourself a new president.
		In light of the failure—a second time—to count all the votes, that won't be necessary.
	www.tompaine.com /articles/kerry_won_.php (1497 words)

	David Wayne JOHNSON v. STATE of Arkansas
		The specific argument is that at the hearing on November 1, 1990, the State claimed to have matched appellant's fingerprints with fingerprints found at the scene, but, in fact, the fingerprintanalysis done at the Crime Laboratory was not completed and mailed to the prosecutor's office until November 26, 1990.
		In this argument appellant contends that the trial court erred in its Rule 37 ruling in refusing to hold that this court improperly applied the harmless error analysis to an evidentiary ruling involving the testimony of Dr. Moneypenny.
		In sum, appellant's argument is without merit because he did not plead the matter in his Rule 37 petition in circuit court, and it is barred.
	courts.state.ar.us /opinions/old/CR94-960A.html (7038 words)

	Jackson v. State (Glaze, J.) CR96-836
		Appellant Alvin Jackson was serving a life sentence without parole in prison for one count of capital murder and two counts of attempted murder when he stabbed a prison guard to death.
		See footnote 1 The Supreme Court and this court have held that for such an argument to prevail under the Equal Protection Clause, the defendant must prove that the decisionmakers in his case acted with discriminatory purpose.
		The trial court denied Jackson's argument, reasoning that the legislature intended to cover two separate aggravating factors by the above provisions, one, the evidence showed Jackson had a prior violent criminal history, and two, the proof also showed he was a prison inmate.
	courts.state.ar.us /opinions/1997b/971009/cr96-836.html (1798 words)

	A.2.1. Scanners
		One of the last five arguments may be used to specify the kind of end test to be used; these are called termination arguments.
		The argument lists-of-lists is viewed as a tree where each internal node is a non-empty list and the elements of the list are the children of the node.
		The type argument is a type specifier indicating the type of values returned by init and step.
	www.music.mcgill.ca /~ferguson/cltl/clm/node350.html (1287 words)

	[No title]
		In analyzing Farrow's double counting argument, the starting point of the inquiry is Appendix A to the Sentencing Guidelines, which specifies the guideline section or sections applicable to the statute of conviction.
		After hearing the argument of Farrow's counsel that alien status is a proper basis for a downward departure, the Court responded that "I think there are times when it can" provide a basis for departure, but that "I simply don't think these circumstances warrant" such a departure.
		His claim that this constituted "double counting" was rejected out of hand: "The language of the aggravated assault provision clearly provides for a calibrated adjustment of the offense level according to the use made of the dangerous weapon and, as such, does not double count." Couch, 1995 WL 369318, **9 (emphasis supplied).
	www.michbar.org /opinions/us_appeals/1999/120899/5747.html (9983 words)

	Counting Money (Site not responding. Last check: 2007-10-26)
		Other counting money views, such as the those summarized in Buddhist concept of tanha, suggest trivial attachments are at the root of much human suffering.
		The touchstone allowed you to estimate the amount of gold counting money in an alloy, which was then multiplied by the weight to find the amount of gold alone in a lump.
		The dictionary definition of addiction is "Addiction is a strong dependence on a drug typified by three factors: 1) severe withdrawal symptoms; 2) tolerance to a given dose, or the need for more and more of the substance; and 3) the loss of control.
	money.hostrim.com /counting-money.html (906 words)

	Combinatorics -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-26)
		Combinatorics is a branch of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics that studies finite collections of objects that satisfy specified criteria.
		In particular, it is concerned with "counting" the objects in those collections (enumerative combinatorics) and with deciding whether certain "optimal" objects exist (extremal combinatorics) and which "algebraic" structures these objects have (algebraic combinatorics).
		An alternate proof works by (additional info and facts about double counting) double counting: count the number of ordered triples of people (A,B,C) where person B knows person A but does not know person C. Suppose person K knows k of the 5 others.
	www.absoluteastronomy.com /encyclopedia/c/co/combinatorics.htm (1325 words)

	02-1189 -- U.S. v. Cardena-Garcia -- 03/26/2004
		Appellants' arguments might wash had they pled to a lesser offense and § 2L1.1(b)(6)(4) was being considered as a relevant conduct enhancement.
		Impermissible double counting "occurs when the same conduct on the part of the defendant is used to support separate increases under separate enhancement provisions which necessarily overlap, are indistinct, and serve identical purposes." United States v.
		We recognize the double counting argument made by Appellants is not the one we addressed in United States v.
	www.kscourts.org /ca10/cases/2004/03/02-1189.htm (1549 words)

	E.W. Dijkstra Archive: For the record: painting the squared plane (EWD1212)
		In short, for an impossibility argument it is very tempting to try to get away with the simplicity of a counting argument.
		Counting red squares is too crude: their number increases by 1 at a time, which is only mildly interesting; worse is that the notion "red square" says nothing about the notion of being neighbours.
		The final argument nicely illustrates the linguistic demands that the doing of mathematics makes: a term for what we called "pink edges" is absolutely essential.
	www.cs.utexas.edu /~EWD/transcriptions/EWD12xx/EWD1212.html (599 words)

	The Kalam Cosmological Argument Yet Again: The Question of the Metaphysical Possibility of an Infinite Temporal Series
		The argument by William Lane Craig that an actual infinite set of real entities is metaphysically impossible depends upon his successfully maintaining that the application of Cantorian set theory to the real world generates counterintuitive absurdities.
		In this article, I turn my attention to Craig's argument that any infinite temporal series of past temporal intervals[7] or events[8] is metaphysically impossible, even though it is to be assumed arguendo that some real infinites are metaphysically possible.
		The notion of traversing necessarily pertains to some one and the same entity crossing, passing or going through all the members of a collection, one-by-one.[45] Moreover, we can easily conceive of a succession of entities, each of short duration, such that the annihilation of one is the cause of the coming-to-be of its successor.
	www.infidels.org /library/modern/arnold_guminski/kalam2.shtml (8642 words)

	Could an Infinite Series of Past Events
		I shall try to show that the standard criticisms of this argument are correct, and that Craig’s attempts to defend it against those criticisms are unsuccessful.
		He suggests that if it were possible for someo ne to have counted all the negative numbers ending at zero, then it would also be possible to reverse direction and count them all starting from zero.
		"Counting down from infinity" is not well described as "turning around and running in the opposite direction." This sounds like the definition of a series that does have a beginning–a series that "begins" when one "turns around," w hereas the count from infinity has no beginning.
	stripe.colorado.edu /~morristo/infpast.html (6005 words)

	William McClure
		Argument classifiers may float away from their NP giving hon-o 3.satu, while adjunct classifiers may not, and *mise-de san.ken at 3 stores [lit: store-at 3.buildings] is bad (Inoue 1978).
		Both arguments and adjuncts allow the XP-internal [xp[qp ]-particle] structure, although it should be noted that the classifying element is actually optional.
		Agreement between the classifer and the direct object is forced by the fact that the variable in the classifer and the variable in the predicate must be the same.
	www.ling.upenn.edu /Events/PLC/plc23/mcclure.html (1088 words)

	Personal Page for Scott Watson
		Lacking the exact equations of string theory, they showed from a simple counting argument that three dimensions was the maximum number that could expand under this process.
		This argument was further investigated in the context of Dilaton cosmology.
		If this dimensionality argument is to hold, it must do so for these higher degrees of freedom, such as d-branes.
	www.het.brown.edu /people/watson/pages/statementofresearch.htm (519 words)

	[9] Compression of random data (WEB, Gilbert and others) (Site not responding. Last check: 2007-10-26)
		The "counting argument" is actually the proof of the theorem.] The WEB compressor (see details in section 9.3 below) was claimed to compress without loss all files of greater than 64KB in size to about 1/16th their original length.
		All schemes are subject to the counting argument.
		Another common (but still incorrect) argument is to assume that for any file, some still to be discovered algorithm might find a seed for a pseudo-random number generator which would actually generate the whole sequence of bytes contained in the file.
	www.faqs.org /faqs/compression-faq/part1/section-8.html (4166 words)

	The crossing number of the complete graph (Site not responding. Last check: 2007-10-26)
		A vertex on the top is connected to one on the bottom with a lateral line segment of minimum possible positive winding number around the cylinder.
		This follows from an argument counting (with multiplicities) the number of crossings in a drawing of all K(n-1)'s contained in an optimal drawing of K(n).
		His result is based on a counting argument similar to that described above.
	www.emba.uvm.edu /~archdeac/newlist/crosskn.htm (337 words)

	Random Data
		However, it is possible that this counting argument is being wrongly applied to compressed data.
		Thus being the proof for an argumentative outcome that it is impossible.
		I shall write more on the fallacy of the counting argument in a few days and why I think that these proponents have stiffled creative thought in the field of data compression.
	www.codecomments.com /message257888.html (2074 words)

	Function - Questionz.net , answers to all your questions (Site not responding. Last check: 2007-10-26)
		The object x is called the argument of the function f, and y is said to "depend functionally" on x.
		The most familiar kind of function is that where the argument and the function's value are both numbers, and the functional relationship is expressed by a formula, and the value of the function is obtained from the arguments by direct substitution.
		This counting argument shows that there are functions from integers to integers that are not computable.
	www.questionz.net /Family/Function.html (2540 words)

	Compound (JPL-3.0.3-alpha API)
		Atom is a subclass of Compound, whose instances have zero arguments.
		Direct instances of Compound must have one or more arguments (it is an error to attempt to construct a Compound with zero args; a JPLException will be thrown).
		Note the use of the "anonymous array" notation to denote the arguments (an anonymous array of Term).
	www.swi-prolog.org /packages/jpl/java_api/javadoc/jpl/Compound.html (522 words)

	USCA1 Opinion 04-1089
		First, he argues that the district court's application of a cross reference in U.S.S.G. § 2G2.4(c)(2), and further application of a sentence enhancement in U.S.S.G. § 2G2.2(b)(2)(E), constituted impermissible double punishment (or "double counting") for the same conduct.
		The premise of Foster's double counting argument is that both the cross reference and the enhancement were triggered by his emailing to others images of child pornography that he previously had received on his computer.
		And there is no double counting when different components or aspects of the relevant criminal conduct trigger different Guidelines provisions which increase one's base offense level.
	www.ca1.uscourts.gov /cgi-bin/getopn.pl?OPINION=04-1089.01A (417 words)

	National Review: Census and citizenship - argument against counting illegal aliens for purposes of congressional ...
		Sometime before the end of the year, the House of Representatives is likely to address one of the most outrageous of all federal policies-the counting of illegal aliens in the census for purposes of congressional apportionment.
		In 1980, an estimated two million illegal aliens were included in the count; on the same basis, that figure today is estimated to have risen to over six million.
		Rather, the phrase "in each state" has been viewed, since the time of the Framers, as communicating the idea that the persons to be counted "belonged" to the state in some comprehensible way.
	www.findarticles.com /p/articles/mi_m1282/is_n18_v41/ai_7962239 (607 words)

	A counting argument
		This thus determines the minimum length of a sequence from which self-calibration can be obtained, depending on the type of constraints which are available for each view.
		Of course this counting argument is only valid if all the constraints are independent.
		In this context critical motion sequences are of special importance (see Section 6.2.5).
	www.cs.unc.edu /~marc/tutorial/node85.html (139 words)

	[No title]
		Despite the argument direction, the POA assumes that etherealize consumes the Servant argument, and does not access a Servant in any way after it has been passed to etherealize.
		Despite the argument direction, the POA assumes that postinvoke consumes the Servant argument, and does not access a Servant in any way after it has been passed to postinvoke.
		The POA does not increment or decrement the reference count of the Servant passed to this function.
	www.omg.org /issues/issue1735.txt (2192 words)

	On the Bottleneck Counting Argument (ResearchIndex) (Site not responding. Last check: 2007-10-26)
		Abstract: Both the bottleneck counting argument [7, 8] and Razborov's approximation method [1, 4, 12] have been used to prove exponential lower bounds for monotone circuits.
		We show that under the monotone circuit model for every proof by the approximation method, there is a bottleneck counting proof and vice versa.
		We also illustrate the elegance of the bottleneck counting technique with a simple self-explained example: the proof of a (previously known) lower bound for the 3-CLIQUEn problem by the...
	citeseer.ist.psu.edu /299764.html (405 words)

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