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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 [1] [2] and extended by Edward J. McCluskey in 1956. [3]
Since, in general, there are two choices for each square root, it might look as if this provides 8 (= 2 3) choices for the set {r 1, r 2, r 3, r 4}, but, in fact, it provides no more than 2 such choices, because the consequence of replacing one of the square roots by the symmetric one is that the set {r 1, r 2, r 3, r 4} becomes the set {−r 1 ...
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
More precisely, a binary operation on a set is a mapping of the elements of the Cartesian product to : [1] [2] [3] f : S × S → S . {\displaystyle \,f\colon S\times S\rightarrow S.} The closure property of a binary operation expresses the existence of a result for the operation given any pair of operands.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
Second edition of the book. Neil Sloane started collecting integer sequences as a graduate student in 1964 to support his work in combinatorics. [8] [9] The database was at first stored on punched cards.