The exponential function is a mathematical function denoted by or . Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the operation of taking powers of a number, but various modern definitions allow it to be rigorously extended to all real arguments , including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to consider the exponential function to be "the most important function in mathematics".
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1.
A parameter, generally, is any characteristic that can help in defining or classifying a particular system. That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
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. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.
In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced "A equals B". The symbol "=" is called an "equals sign". Two objects that are not equal are said to be distinct.
In mathematics, the term linear is used in two distinct senses for two different properties:
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. The terms are opposites. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder, or a wildcard character that stands for an unspecified symbol.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
In computer programming, a parameter or a formal argument is a special kind of variable used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters.
The syntax of the C programming language is the set of rules governing writing of software in C. It is designed to allow for programs that are extremely terse, have a close relationship with the resulting object code, and yet provide relatively high-level data abstraction. C was the first widely successful high-level language for portable operating-system development.
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
In mathematics, a variable is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
This is an overview of Fortran 95 language features. Included are the additional features of TR-15581:Enhanced Data Type Facilities, which have been universally implemented. Old features that have been superseded by new ones are not described – few of those historic features are used in modern programs although most have been retained in the language to maintain backward compatibility. The current standard is Fortran 2023; many of its new features are still being implemented in compilers. The additional features of Fortran 2003, Fortran 2008, Fortran 2018 and Fortran 2023 are described by Metcalf, Reid, Cohen and Bader.
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value. The term can take on several different meanings depending on the context. For example:
This article compares a large number of programming languages by tabulating their data types, their expression, statement, and declaration syntax, and some common operating-system interfaces.
In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance ; as a noun, it has two different meanings:
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact.
The mathematical concept of a function dates from the 17th century in connection with the development of the calculus; for example, the slope of a graph at a point was regarded as a function of the x-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme.
