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The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values. [1] [2] For example, if the function f is defined by f (x) = 2 x 2 – 3 x + 1, then assigning the value 3 to its argument x yields the function value 10, since f (3) = 2·3 2 – 3·3 + 1 = 10.
In fact the absolute value is the "only" norm on , in the sense that, for every norm ‖ · ‖ on , ‖ x ‖ = ‖ 1 ‖ ⋅ | x |. The complex absolute value is a special case of the norm in an inner product space , which is identical to the Euclidean norm when the complex plane is identified as the Euclidean plane R 2 {\displaystyle \mathbb ...
A specific element x of X is a value of the variable, and the corresponding element of Y is the value of the function at x, or the image of x under the function. A function f, its domain X, and its codomain Y are often specified by the notation :.
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The letter may be followed by a subscript: a number (as in x 2), another variable (x i), a word or abbreviation of a word (x total) or a mathematical expression (x 2i + 1). Under the influence of computer science, some variable names in pure mathematics consist of several letters and digits.