Transcription of 3 Binary Operations - Arkansas Tech University
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3 Binary Operations - Arkansas Tech University
Arkansas Tech UniversityMATH 4033: Elementary Modern AlgebraDr. Marcel B. Finan3 Binary OperationsWe are used to addition and multiplication of real numbers. These operationscombine two real numbers to generate a unique single real number. So wecan look at these Operations as functions on the setR R={(a, b) :a Rand b R}defined by+ :R R R(a, b) a+band :R R R(a, b) a bThese Operations are examples of a Binary operation. The general definitionof a Binary operation is as operationon a set S is a mapping that assigns to each orderedpair of elements ofSa uniquely determined element is, :S S Sis a mapping. The setSis said to beclosedunder the operation .The image (a, b) will be denoted bya and multiplication are Binary Operations on the setZof integersso that this set is closed under these Operations .
MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan 3 Binary Operations We are used to addition and multiplication of real numbers. These operations combine two real numbers to generate a unique single real number. So we can look at these operations as functions on the set R×R = {(a,b) : a ∈ R and b ∈ R} defined by + : R×R −→ R
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