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Consistency
ConsistencyMathematics contains a number of different systems, but each mathematical system, no matter how different it may be from another, has consistency as one of its goals. When a mathematical system is consistent, a statement and the opposite, or negation, of that same statement cannot both be proven true. For example, in the familiar system of algebra, it is true that a + 1 > a. Even if a is a negative number, or 0, the statement is true. For example, −3.5 + 1 is −2.5, and −2.5 is greater than −3.5 (because −2.5 is to the right of −3.5 on a number line). Because this system is consistent, it is not possible to prove that a + 1 is less than a or equal to a. Consistency is also important in the use of mathematical definitions and symbols. For example, (5)2 equals 25 and (−5)2 also equals 25. Is the square root of 25 equal to 5 or to 5? The answer is both: 5 is the square root of 25, and 5 is also the square root of 25. However, for consistency, the symbol for square root , has been defined to mean only the positive square root, if one exists. So has only one value (5) even though the equation x 2 = 25 has two roots, or solutions. In solving this equation, you must add the ± symbol to the radical symbol to show that both the positive and negative roots are desired. x2 = 25 Equation to be solved x = ± Taking the square root of both sides x = 5 or −5 The two solutions The second step uses the rule that the square root can be taken of both sides of an equation, and the equation will still be true. Is it always true that, if a 2 = b 2, then a = b ? Consider the following example. (−3)2 = (3)2 This is true because 9 = 9 Taking the square root of both sides -3 = 3 This is not true What went wrong? If a 2 = b 2, then a = b is consistently true only when a and b are both positive numbers. This means that this rule is true (and the system maintains consistency) if it is written as a 2 = b 2 means a = b when a, b ≥ 0. When moving beyond the familiar systems of ordinary arithmetic and algebra, consistency poses some difficult challenges. For example, many mathematicians have wrestled with the sentence "This statement is not provable." If the statement is provable, it is false (a contradiction!); if it is true, it is not provable. The work of the mathematicians David Hilbert, Kurt Gödel, Douglas Hofstadter, and Raymond Smullyan delve into this puzzle. see also Proof. Lucia McKay BibliographyEves, Howard, and Carroll V. Newsom. An Introduction to the Foundations and Fundamental Concepts of Mathematics. New York: Holt, Rinehart, and Winston, 1965. Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1999. Reid, Constance. Hilbert. Berlin: Springer-Verlag, 1970. Smullyan, Raymond M. What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles. Englewood Cliffs, NJ: Prentice-Hall, 1978. |
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McKay, Lucia. "Consistency." Mathematics. 2002. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. McKay, Lucia. "Consistency." Mathematics. 2002. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1G2-3407500074.html McKay, Lucia. "Consistency." Mathematics. 2002. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1G2-3407500074.html |
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consistency
consistency Used to describe the property of a DISTRIBUTED TRANSACTION. It describes the fact that such a transaction must transform a DISTRIBUTED SYSTEM from one state to another consistent state. For example, in a banking system an account balance should be equal to the old balance of the account plus the sum of the credits minus the sum of the debits on the account. If this condition did not hold, for example because of a hardware error occurring when a transaction took place, then the bank database would not be consistent: it would show a number of credits, a number of debits and a new bank balance which would be inconsistent with respect to each other. This is an important property of a distributed system along with ATOMICITY, ISOLATION and DURABILITY. See also ACID.
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DARREL INCE. "consistency." A Dictionary of the Internet. 2001. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. DARREL INCE. "consistency." A Dictionary of the Internet. 2001. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O12-consistency.html DARREL INCE. "consistency." A Dictionary of the Internet. 2001. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O12-consistency.html |
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consistency
con·sist·en·cy / kənˈsistənsē/ (also con·sist·ence / -təns/ ) • n. (pl. -cies) 1. conformity in the application of something, typically that which is necessary for the sake of logic, accuracy, or fairness: the grading system is to be streamlined to ensure greater consistency. ∎ the achievement of a level of performance that does not vary greatly in quality over time. 2. the way in which a substance, typically a liquid, holds together; thickness or viscosity: the sauce has the consistency of creamed butter. |
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"consistency." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "consistency." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O999-consistency.html "consistency." The Oxford Pocket Dictionary of Current English. 2009. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O999-consistency.html |
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consistency
consistency A term used in the context of methods for ordinary and partial differential equations. A formula derived from a discretization is consistent if the order is at least one with respect to the stepsize, h. Consistency is a necessary condition for convergence of a discretization formula (see error analysis).
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JOHN DAINTITH. "consistency." A Dictionary of Computing. 2004. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. JOHN DAINTITH. "consistency." A Dictionary of Computing. 2004. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O11-consistency.html JOHN DAINTITH. "consistency." A Dictionary of Computing. 2004. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O11-consistency.html |
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consistency
consistency See CONSISTENCE.
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AILSA ALLABY and MICHAEL ALLABY. "consistency." A Dictionary of Earth Sciences. 1999. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. AILSA ALLABY and MICHAEL ALLABY. "consistency." A Dictionary of Earth Sciences. 1999. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O13-consistency.html AILSA ALLABY and MICHAEL ALLABY. "consistency." A Dictionary of Earth Sciences. 1999. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O13-consistency.html |
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consistency
consistency See consistence.
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MICHAEL ALLABY. "consistency." A Dictionary of Ecology. 2004. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. MICHAEL ALLABY. "consistency." A Dictionary of Ecology. 2004. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O14-consistency.html MICHAEL ALLABY. "consistency." A Dictionary of Ecology. 2004. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O14-consistency.html |
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consistency
consistency See CONSISTENCE.
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MICHAEL ALLABY. "consistency." A Dictionary of Plant Sciences. 1998. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. MICHAEL ALLABY. "consistency." A Dictionary of Plant Sciences. 1998. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O7-consistency.html MICHAEL ALLABY. "consistency." A Dictionary of Plant Sciences. 1998. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O7-consistency.html |
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consistency
consistency
•radiancy
•immediacy, intermediacy
•expediency • idiocy • saliency
•resiliency • leniency
•incipiency, recipiency
•recreancy • pruriency • deviancy
•subserviency • transiency • pliancy
•buoyancy, flamboyancy
•fluency, truancy
•constituency • abbacy • embassy
•celibacy • absorbency
•incumbency, recumbency
•ascendancy, intendancy, interdependency, pendency, resplendency, superintendency, tendency, transcendency
•candidacy
•presidency, residency
•despondency • redundancy • infancy
•sycophancy • argosy • legacy
•profligacy • surrogacy
•extravagancy • plangency • agency
•regency
•astringency, contingency, stringency
•intransigency • exigency • cogency
•pungency
•convergency, emergency, insurgency, urgency
•vacancy • piquancy • fricassee
•mendicancy • efficacy • prolificacy
•insignificancy • delicacy • intricacy
•advocacy • fallacy • galaxy
•jealousy, prelacy
•repellency • valency • Wallasey
•articulacy • corpulency • inviolacy
•excellency • equivalency • pharmacy
•supremacy • clemency • Christmassy
•illegitimacy, legitimacy
•intimacy • ultimacy • primacy
•dormancy • diplomacy • contumacy
•stagnancy
•lieutenancy, subtenancy, tenancy
•pregnancy
•benignancy, malignancy
•effeminacy • prominency
•obstinacy • pertinency • lunacy
•immanency
•impermanency, permanency
•rampancy • papacy • flippancy
•occupancy
•archiepiscopacy, episcopacy
•transparency • leprosy • inerrancy
•flagrancy, fragrancy, vagrancy
•conspiracy • idiosyncrasy
•minstrelsy • magistracy • piracy
•vibrancy
•adhocracy, aristocracy, autocracy, bureaucracy, democracy, gerontocracy, gynaecocracy (US gynecocracy), hierocracy, hypocrisy, meritocracy, mobocracy, monocracy, plutocracy, technocracy, theocracy
•accuracy • obduracy • currency
•curacy, pleurisy
•confederacy • numeracy
•degeneracy • itinerancy • inveteracy
•illiteracy, literacy
•innocency • trenchancy • deficiency
•fantasy, phantasy
•intestacy • ecstasy • expectancy
•latency • chieftaincy • intermittency
•consistency, insistency, persistency
•instancy • militancy • impenitency
•precipitancy • competency
•hesitancy • apostasy • constancy
•accountancy • adjutancy
•consultancy, exultancy
•impotency • discourtesy
•inadvertency • privacy
•irrelevancy, relevancy
•solvency • frequency • delinquency
•adequacy • poignancy
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"consistency." Oxford Dictionary of Rhymes. 2007. Encyclopedia.com. 30 May. 2012 <http://www.encyclopedia.com>. "consistency." Oxford Dictionary of Rhymes. 2007. Encyclopedia.com. (May 30, 2012). http://www.encyclopedia.com/doc/1O233-consistency.html "consistency." Oxford Dictionary of Rhymes. 2007. Retrieved May 30, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O233-consistency.html |
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