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Mean value: If x is a variable that takes its values in some sequence of numbers S, then ¯ may denote the mean of the elements of S. 5. Negation : Sometimes used to denote negation of the entire expression under the bar, particularly when dealing with Boolean algebra .
If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.
h.c. – Hermitian conjugate, often used as part of + h.c. (Also written as H.c.) hcc – hacovercosine function. (Also written as hacovercos.) hcv – hacoversine function. (Also written as hacover, hacovers.) hcf – highest common factor of two numbers. (Also written as gcd.) H.M. – harmonic mean. HOL – higher-order logic. Hom – Hom ...
In this case, an element x of the domain is represented by an interval of the x-axis, and the corresponding value of the function, f(x), is represented by a rectangle whose base is the interval corresponding to x and whose height is f(x) (possibly negative, in which case the bar extends below the x-axis).
A statement such as that predicate P is satisfied by arbitrarily large values, can be expressed in more formal notation by ∀x : ∃y ≥ x : P(y). See also frequently. The statement that quantity f(x) depending on x "can be made" arbitrarily large, corresponds to ∀y : ∃x : f(x) ≥ y. arbitrary A shorthand for the universal quantifier. An ...
By this construction, the function that defines the harmonic number for complex values is the unique function that simultaneously satisfies (1) H 0 = 0, (2) H x = H x−1 + 1/x for all complex numbers x except the non-positive integers, and (3) lim m→+∞ (H m+x − H m) = 0 for all complex values x.
An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.
the argument of a complex number in mathematics; the value of a plane angle in physics and mathematics; the angle to the z axis in spherical coordinates (mathematics) epoch or phase difference between two waves or vectors; the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (physics) latitude in geodesy; radiant flux ...