M
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magic square
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May be read at http://www.harcourt.com/dictionary /browse/19/
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magnitude
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May be read at http://www.harcourt.com/dictionary /browse/19/
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main diagonal
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May be read at http://www.harcourt.com/dictionary /browse/19/
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major arc
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May be read at http://www.harcourt.com/dictionary /browse/19/
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major axis
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May be read at http://www.harcourt.com/dictionary /browse/19/
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majority
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Mandelbrot set
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May be read at http://www.harcourt.com/dictionary /browse/19/
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manifold
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mantissa
.
Given a real number written in decimal notation, such as 1.333333..., the digits following the decimal point are comprehended under the label "mantissa". (PL characteristic.) This term is more commonly applied to a portion of the logarithm (PL) of a number, and is obtained from logarithmic tables.
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map
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mapping
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Markov chain
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Markov process
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May be read at http://www.harcourt.com/dictionary /browse/19/
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marriage theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Maschke's theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matching
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matching number
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mathematical induction
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mathematical model
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mathematical probability
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mathematical table
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Mathieu equation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix algebra tableau
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix calculus
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix game
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix of a linear transformation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix of a system of linear equations
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matrix theory
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May be read at http://www.harcourt.com/dictionary /browse/19/
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matroid
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May be read at http://www.harcourt.com/dictionary /browse/19/
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(lattice) max
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Union (PL) of all atoms (PL) of a lattice. Tt's indicator table contains all ones except for the row of zeros for all atoms. It is usually designated as the 1 of the lattice (invoking confusion with ones of indicator table). It is an ideal or arbitrary element, unattainable by any finite operation. Designated herein as MAX. (PL min.)
max-flow min-cut theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximal
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximal planar graph
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximal with respect to property P
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximax criterion
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maxim criterion
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximization
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximum
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximum condition
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximum-modulus theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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maximum with respect to property P
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May be read at http://www.harcourt.com/dictionary /browse/19/
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meager set
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mean
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Usually applied to the "middle" of a number sequence (PL) as its "average" (PL) or representative. Thus, the arithmetic mean occupies "the middle" of an arithmetic progression (PL); the geometric mean occupies "the middle" of a geometric progression (PL); the harmonic mean occupies "the middle" of a harmonic progression (PL); etc. Among other uses of the term, "mean value theorem of the differential calculus" (PL).
mean curvature
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mean proportional
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May be read at http://www.harcourt.com/dictionary /browse/19/
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means
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mean value theorem
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(PL Gauss mean value theorem.)
measurable function
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measurable set
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measurable space
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measure
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measurement scales, theory of
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"The Theory of Measurement Scales" was initiated in 1940 by the Harvard psychophysicist, S. S. Stevens: (1) defining the scale in terms of that mathematical transformation (PL)leaving the scale invariant; and (2) associating it with allowable statistics.
measure ring
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measure space
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May be read at http://www.harcourt.com/dictionary /browse/19/
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measure zero
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May be read at http://www.harcourt.com/dictionary /browse/19/
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median
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The "middle" of an ordering of numbers, hence, the average (representative) of a set of ordinal measures (PL).
mediation-duplation multiplication
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An ancient method of multiplication, used by the Egyptians and mentioned in The Bible (xxxx). The term mediation-duplation means "halving-doubling". Given two numbers (such as 37 and 28) to multiply, one number was mediated/halved (say, the smaller one, 28 -> 14), while the other was duplated/doubled (37 -> 74). Continuing: 14 -> 7, 74 -> 148; 7 -> 3 (rounding down), 148 -> 296; 3 -> 1 (rounding down), 296 -> 592. The process concludes at the halving to 1. You will note that any odd halving is underlined, along with its corresponding double. Only these duplates (corresponding to the odd halvings) are added: 148 + 296 + 592 = 1036. If you perform the multiplication in the standard way, you find 37 x 28 = 1036. The reason behind this method is that odd numbers in binary notation end in 1, while even numbers in binary end in 0. This means that, implicitly, the addition involves 1 times odd-associated-duplate and 0 times even-asociated-duplate. So it anticipates the binary notation and arithmetic as well as binary logic circuits -- which found application in computers. (Note also that this method is antitonic, PL.)
member
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Menelaus' theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Menger's theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mensuration
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May be read at http://www.harcourt.com/dictionary /browse/19/
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meromorphic function
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May be read at http://www.harcourt.com/dictionary /browse/19/
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metamathematics
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May be read at http://www.harcourt.com/dictionary /browse/19/
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metric
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May be read at http://www.harcourt.com/dictionary /browse/19/
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metric space
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May be read at http://www.harcourt.com/dictionary /browse/19/
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metric tensor
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May be read at http://www.harcourt.com/dictionary /browse/19/
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metrizable space
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Meusnier's theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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micro-
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May be read at http://www.harcourt.com/dictionary /browse/19/
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midpoint
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mil
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May be read at http://www.harcourt.com/dictionary /browse/19/
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milli-
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A prefix derived from Latin, applied in measurements to one-thousandths part, as in "millimeter" for "one thousandths of a meter" (of length).
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million
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A number which is written in decimal base (PL) notation as 1,000,000; in exponential notation (PL) as 106.
(lattice) min
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The intersection (PL) of all atoms (PL) of a lattice. It's indicator table (PL) ("truth table") contains all zeros except for the row of all ones for all atoms. It is usually designated as the 0 of a lattice (resulting in confusion with zeros of an indicator table), and is an an ideal or arbitrary value, unattainable by finite lattice operations. The latter is herein labeled as MIN. (PL max.)
minimal connector problem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minimal equation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minimal polynomial
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minimal surface
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minimization
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May be read at http://www.harcourt.com/dictionary /browse/19/
minimum
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minimum condition
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Minkowski space
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minor
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minor arc
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minor axis
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minor of a graph
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minuend
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May be read at http://www.harcourt.com/dictionary /browse/19/
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minus
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The name of the symbol used in the operation (PL) of subtraction (PL). (Thus, 4 - 3 is verbalized as "four minus three".) The term is frequently misused in reference to a negative number (PL below).
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minus number
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As in "minus 4" or "minus 11". Serious misnomer, however prevalent. The predicate "minus 3" is as antithetic as the predicate "a married batchelor", since both parenthetically predicate that "2 = 1". For "marriage" is a relation between two adult persons, predicating twoness, whereas "batchelor" predicates "unmarried oneness". Similarly, the term "minus" labels the binary operation of arithmetic subtraction, predicating a "twoness" relating minuend and a subtrahend (PL), whereas its numeric attributive predicates "oneness". Instead of saying "minus number", say "negative number". The distinction can be reinforced by continuing to write as medial the subtraction sign, and writing as superscript prefix the negative sign, as in -3.
minused
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Slang expression for the operation of subtraction (PL), as in saying "I minused the total by 7".
minute
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mixed-base notation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mixed decimal
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mixed graph
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mixed number
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mixing transformation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Möboid (Möius band/strip)
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A surface that is not orientable (PL), modeled by half-twisting a rectangular strip and gluing the ends together. Without the half-twist, the surface is a cylinder (PL), which can topologically factor as the Cartesian product (PL): C x L, where C is a circle, and L a line segment -- that is, a cylinder is a stack of circles, equivalently, a revolution of line segments -- as such being orientable with two sides between boundaries. But the half-twisting destroys orientability, resulting in a one-sided structure so that you pass from "one side" to another without crossing a boundary. In fiber bundle (PL) language, the cylinder is a trivial fiber bundle, but the möboid is a nontrivial or proper fiber bundle. (PL A möbius stripper and a möboid subway system[30].)
Möbius function
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May be read at http://www.harcourt.com/dictionary /browse/19/
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M&öbius transformation
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May be read at http://www.harcourt.com/dictionary /browse/19/
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mode
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The most frequent value(s) of a set of numbers. It represents a set of typological measures (PL). The average (representative) is unique, except in the case of the mode: a set may have more than one mode.
modern algebra
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May be read at http://www.harcourt.com/dictionary /browse/19/
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modified Bessel functions
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May be read at http://www.harcourt.com/dictionary /browse/19/
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modul
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An arithmetic system (PL Number Theory and Its History, O. Ore, p. 159) closed under addition, subtraction, such as the integers, rationals, real, complex numbers (as scalars). (PL larutan, integral domain, ring, field, bimodul.) The term "modul" is related to "modulus" in congruence theory (PL) since an integral modul consists of all multiples 0, ±m, ±2m, ...: the zero residue class (mod m), i.e., the set of all numbers a for which the congruence a = 0 (mod m) holds. (PL bimodul.)
modular arithmetic
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Introduced by the great German mathematician, Karl Friedrich Gauss (1777-1855). The notion of modulus is applied as an equivalence relation (PL) to create the equivalence class (PL) of all integers yielding the same remainder when divided by a specified divisor labeled "mod". (As an example, 6 = 1 mod 5 ("six is congruent to 1 mod 5", that is, "6 divided by 5 yields remainder 2"). The equivalence class created by the equivalence relation of congruence is denoted as Ci, for i = 0, 1, 2, ..., m - 1. This converts "an infinity of integers" to a finite set wherein each Ci has an additive inverse, forming an additive group. Example (mod 5):
ADDITIVE GROUP mod 5
+
C0
C1
C2
C3
C4
C0
C0
C1
C2
C3
C4
C1
C1
C2
C3
C4
C0
C2
C2
C3
C4
C0
C1
C3
C3
C4
C0
C1
C2
C4
C4
C0
C1
C2
C3
The tragic young French genius, Évariste Galois (1811-32), developed the condition that the use of a prime modulus results in equivalence classes that have multiplicative inverses, forming a multiplicative group. Example (mod 5):
MULTIPLICATIVE GROUP mod 5
*
C0
C1
C2
C3
C4
C0
C0
C0
C0
C0
C0
C1
C0
C1
C2
C3
C4
C2
C0
C2
C4
C1
C3
C3
C0
C3
C1
C4
C2
C4
C0
C4
C3
C2
C1
The result is a finite field (PL), comparable to the rationals (fractions). Today "Galois fields" provide an efficient coding for satellite signals bring us TV news and entertainment from "across the world"!
modular form
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May be read at http://www.harcourt.com/dictionary /browse/19/
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module
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May be read at http://www.harcourt.com/dictionary /browse/19/
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modulo
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May be read at http://www.harcourt.com/dictionary /browse/19/
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modulus of continuity
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Mohr's eigenvector algorithm[1,p.273]
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An algorithm (PL) taught in engineering schools for solving the 2 x 2 case. The primary problem of mathematical physics is to extend this algorithm.
read at http://www.harcourt.com/dictionary /browse/19/.
monic polynomial
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May be read at http://www.harcourt.com/dictionary /browse/19/
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monodromy theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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monoid
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A semigroup with an identity element. (PL up these terms.)
monotone
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May be read at http://www.harcourt.com/dictionary /browse/19/
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monotone convergence theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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monotonic
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May be read at http://www.harcourt.com/dictionary /browse/19/
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monotonicity theorem
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Moore-Smith convergence
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May be read at http://www.harcourt.com/dictionary /browse/19/
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morphism
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May be read at http://www.harcourt.com/dictionary /browse/19/
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Morse theory
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May be read at http://www.harcourt.com/dictionary /browse/19/
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moving frame
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multidimensional derivative
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multilinear algebra
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multilinear form
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multilinear function
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multinomial
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple edges
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple integral
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple point
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple root
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiple-valued
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiplicand
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An operand (PL) in the binary operation of multiplication (PL).
multiplication
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Repeated adding can be tedious -- as in 2 + 2 + 2 = 6. Hence, as a shortcut, the successor function (PL) of recursion (PL) -- used to define counting and addition -- is invoked to define recursively the (binary) operation of multiplication of natural numbers (PL): a * 1 = a, S(a * b) = a * b + a. Multiplication is shown to be a total operation of the natural number system -- hence, of successive systems -- always yielding a natural number. And commutative and associative laws for multiplication can be derived, and it can be shown to distribute (PL) with addition (PL). Since it is welldefined (PL) and commutative, multiplication has a single inverse (PL), namely, division (PL).
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multiplicative function
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiplicative set
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiplicity
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiplier
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The operation (PL) of multiplication has the format: multiplicand * multiplier = product.
multiply
.
The verbal form for the operation (PL) of multiplication.
multiply connected
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May be read at http://www.harcourt.com/dictionary /browse/19/
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multiproduct (multivector)
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xxxxxxx. (PL innerproduct and outerproduct.)