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associative law
associative law in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9. More generally, in addition, for any three numbers a, b, and c the associative law is expressed as ( a + b )+ c = a +( b + c ). Multiplication of numbers is also associative, i.e., ( a × b )× c = a ×( b × c ). In general, any binary operation, symbolized by ∘, joining mathematical entities A, B, and C obeys the associative law if ( A ∘ B )∘ C = A ∘( B ∘ C ) for all possible choices of A, B, and C. Not all operations are associative. For example, ordinary division is not, since (60÷12)÷3=5÷3=5/3, while 60÷(12÷3)=60÷4=15. When an operation is associative, the parentheses indicating which quantities are first to be combined may be omitted, e.g., (2+3)+4=2+(3+4)=2+3+4. |
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"associative law." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>. "associative law." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. (May 27, 2012). http://www.encyclopedia.com/doc/1E1-assoc-law.html "associative law." The Columbia Encyclopedia, 6th ed.. 2011. Retrieved May 27, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1E1-assoc-law.html |
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associative law
associative law Rule of combination in mathematics, in which the result of two or more operations on terms does not depend on the way in which they are grouped. Thus, normal addition and multiplication of numbers follows the associative law, since a + (b + c) = (a + b) + c, and a × (b × c) = (a × b) × c.
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"associative law." World Encyclopedia. 2005. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>. "associative law." World Encyclopedia. 2005. Encyclopedia.com. (May 27, 2012). http://www.encyclopedia.com/doc/1O142-associativelaw.html "associative law." World Encyclopedia. 2005. Retrieved May 27, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O142-associativelaw.html |
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associative law
associative law See associative operation.
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JOHN DAINTITH. "associative law." A Dictionary of Computing. 2004. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>. JOHN DAINTITH. "associative law." A Dictionary of Computing. 2004. Encyclopedia.com. (May 27, 2012). http://www.encyclopedia.com/doc/1O11-associativelaw.html JOHN DAINTITH. "associative law." A Dictionary of Computing. 2004. Retrieved May 27, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O11-associativelaw.html |
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