Information about Expression (mathematics)
An expression is a combination of numbers, operators, grouping symbols (such as brackets and parentheses) and/or free variables and bound variables arranged in a meaningful way which can be evaluated. Bound variables are assigned values within the expression (they are for internal use) while free variables can take on values from outside the expression.
For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the expression may be undefined. Thus an expression represents a function whose inputs are the values assigned the free variables and whose output is the resulting value of the expression.
For example, the expression
evaluated for x = 10, y = 5, will give 2; but is undefined for y = 0.
The evaluation of an expression is dependent on the definition of the mathematical operators and on the system of values that is its context.
Two expressions are said to be equivalent if, for each combination of values for the free variables, they have the same output, i.e., they represent the same function. Example:
The expression
An expression must be well-formed. That is, the operators must have the correct number of inputs, in the correct places. The expression 2 + 3 is well formed; the expression * 2 + is not, at least, not in the usual notation of arithmetic.
Expressions and their evaluation were formalised by Alonzo Church and Stephen Kleene in the 1930s in their lambda calculus. The lambda calculus has been a major influence in the development of modern mathematics and computer programming languages.
One of the more interesting results of the lambda calculus is that the equivalence of two expressions in the lambda calculus is in some cases undecidable. This is also true of any expression in any system that has power equivalent to the lambda calculus.
For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the expression may be undefined. Thus an expression represents a function whose inputs are the values assigned the free variables and whose output is the resulting value of the expression.
For example, the expression
evaluated for x = 10, y = 5, will give 2; but is undefined for y = 0.
The evaluation of an expression is dependent on the definition of the mathematical operators and on the system of values that is its context.
Two expressions are said to be equivalent if, for each combination of values for the free variables, they have the same output, i.e., they represent the same function. Example:
The expression
An expression must be well-formed. That is, the operators must have the correct number of inputs, in the correct places. The expression 2 + 3 is well formed; the expression * 2 + is not, at least, not in the usual notation of arithmetic.
Expressions and their evaluation were formalised by Alonzo Church and Stephen Kleene in the 1930s in their lambda calculus. The lambda calculus has been a major influence in the development of modern mathematics and computer programming languages.
One of the more interesting results of the lambda calculus is that the equivalence of two expressions in the lambda calculus is in some cases undecidable. This is also true of any expression in any system that has power equivalent to the lambda calculus.
See also
External links
- Axiomatic Theory of Formulas - theory of expressions on high abstraction level.
- Plot mathematical expressions this system plots math equations, graphs, diagrams, and even animated cartoons of transformation of math expressions and arithmetic operations. Knowledge of TeX not required.
number is an abstract idea used in counting and measuring. A symbol which represents a number is called a numeral, but in common usage the word number is used for both the idea and the symbol.
..... Click the link for more information.
..... Click the link for more information.
operator is a function, that operates on (or modifies) another function. Often, an "operator" is a function that acts on functions to produce other functions (the sense in which Oliver Heaviside used the term); or it may be a generalization of such a function, as in linear algebra,
..... Click the link for more information.
..... Click the link for more information.
Lie bracket of a Lie algebra is a binary operation denoted by [·, ·] : × → . By using the commutator as a Lie bracket, every associative algebra can be turned into a Lie algebra.
..... Click the link for more information.
..... Click the link for more information.
free variable is a variable referred to in a function that is not a local variable or an argument of that function.
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable
..... Click the link for more information.
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable
..... Click the link for more information.
Evaluation is the process of characterizing and appraising something of interest or of determining the value of an expression (mathematics).
..... Click the link for more information.
Computer science
- determining the value of an expression (programming)
..... Click the link for more information.
function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
..... Click the link for more information.
..... Click the link for more information.
division by zero if the divisor is zero. Such a division can be formally expressed as where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting.
..... Click the link for more information.
..... Click the link for more information.
See also Equivalence
The Equivalent was a sum negotiated at £398,000 paid to Scotland by the English Government under the terms of the Acts of Union 1707. Proposals for it first emerged in the course of abortive Union negotiations in 1702/03.
..... Click the link for more information.
The Equivalent was a sum negotiated at £398,000 paid to Scotland by the English Government under the terms of the Acts of Union 1707. Proposals for it first emerged in the course of abortive Union negotiations in 1702/03.
..... Click the link for more information.
The term "well-formed," refers to the syntactic validity of strings in some language. When used by itself, can refer to:
..... Click the link for more information.
- In logic, a well-formed formula or WFF.
- In programming, syntactic elements of a programming language.
..... Click the link for more information.
Alonzo Church
Alonzo Church (1903–1995)
Born 6/14/1903
Washington, DC, USA
Died 8/11/1995
Residence USA
Nationality USA
Field Mathematics
..... Click the link for more information.
Alonzo Church (1903–1995)
Born 6/14/1903
Washington, DC, USA
Died 8/11/1995
Residence USA
Nationality USA
Field Mathematics
..... Click the link for more information.
Stephen Kleene
Born January 5 1909
USA
Died January 25 1994 (aged 85)
Residence USA
Nationality USA
..... Click the link for more information.
Born January 5 1909
USA
Died January 25 1994 (aged 85)
Residence USA
Nationality USA
..... Click the link for more information.
In mathematical logic and computer science, lambda calculus, also λ-calculus, is a formal system designed to investigate function definition, function application, and recursion.
..... Click the link for more information.
..... Click the link for more information.
A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. Programming languages, like natural languagess, are defined by syntactic and semantic rules which describe their structure and meaning respectively.
..... Click the link for more information.
..... Click the link for more information.
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem.
..... Click the link for more information.
..... Click the link for more information.
An expression in a programming language is a combination of values, variables, operators, and functions that are interpreted (evaluated) according to the particular rules of precedence and of association for a particular programming language, which computes and then
..... Click the link for more information.
..... Click the link for more information.
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.
..... Click the link for more information.
..... Click the link for more information.
Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional
..... Click the link for more information.
..... Click the link for more information.
Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast with the imperative programming style that emphasizes changes in state.
..... Click the link for more information.
..... Click the link for more information.
equation is a mathematical statement, in symbols, that two things are the same (or equivalent). Equations are written with an equal sign, as in
The equation above is an example of an equality: a proposition which states that two constants are equal.
..... Click the link for more information.
- .
The equation above is an example of an equality: a proposition which states that two constants are equal.
..... Click the link for more information.
In mathematics, an inequation is a statement that two objects or expressions are not the same, or do not represent the same value. This relation is written with a crossed-out equal sign, like
..... Click the link for more information.
- x ≠ y.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
