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The American method corrects by attempting to decrease the minuend digit m i+1 by one (or continuing the borrow leftwards until there is a non-zero digit from which to borrow). The European method corrects by increasing the subtrahend digit s i+1 by one.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .
Any monotonically increasing function, by its definition, [9] may be applied to both sides of an inequality without breaking the inequality relation (provided that both expressions are in the domain of that function). However, applying a monotonically decreasing function to both sides of an inequality means the inequality relation would be ...
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called " reducing a fraction ".
A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope.
In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero . Negative numbers are often used to represent the magnitude of a loss or deficiency.
If the domain of definition equals X, one often says that the partial function is a total function. In several areas of mathematics the term "function" refers to partial functions rather than to ordinary functions. This is typically the case when functions may be specified in a way that makes difficult or even impossible to determine their domain.
Although the definition here uses a parameterization of the curve, the notion of asymptote does not depend on the parameterization. In fact, if the equation of the line is a x + b y + c = 0 {\displaystyle ax+by+c=0} then the distance from the point A ( t ) = ( x ( t ), y ( t )) to the line is given by