Search results
Results from the WOW.Com Content Network
Functional programming is the programming paradigm consisting of building programs by using only subroutines that behave like mathematical functions. For example, if_then_else is a function that takes three functions as arguments, and, depending on the result of the first function (true or false), returns the result of either the second or the ...
Functional notation: if the first is the name (symbol) of a function, denotes the value of the function applied to the expression between the parentheses; for example, (), (+). In the case of a multivariate function , the parentheses contain several expressions separated by commas, such as f ( x , y ) {\displaystyle f(x,y)} .
A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.
Using mathematical notation, several ways exist to define continuous functions in the three senses mentioned above. Let f : D → R {\displaystyle f:D\to \mathbb {R} } be a function defined on a subset D {\displaystyle D} of the set R {\displaystyle \mathbb {R} } of real numbers.
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [1]
For example, in trigonometry, this superscript notation represents standard exponentiation when used with trigonometric functions: sin 2 ( x ) = sin( x ) · sin( x ) . However, for negative exponents (especially −1), it nevertheless usually refers to the inverse function, e.g., tan −1 = arctan ≠ 1/tan .
The notation is also used to denote the characteristic function in convex analysis, which is defined as if using the reciprocal of the standard definition of the indicator function. A related concept in statistics is that of a dummy variable .
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 x {\displaystyle x} is denoted exp x {\displaystyle \exp x} or e x {\displaystyle e^{x}} , with the two notations used interchangeably.