Constant (mathematics)

Constant (mathematics)

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In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a constant is a non-varying value, i.e. completely fixed or fixed in the context of use. The term usually occurs in opposition to variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

(i.e. variable quantity), which is a symbol
Symbol
A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...

 that stands for a value
Value (mathematics)
In mathematics, value commonly refers to the 'output' of a function. In the most basic case, that of unary, single-valued functions, there is one input and one output .The function f of the example is real-valued, since each and every possible function value is real...

 that may vary.

In polynomials, polynomial function of degree 2 is generally denoted as

where a, b and c are constants (or parameters), while x is the variable, a placeholder for the argument of the function being studied. A more explicit way to denote this function is

which makes the function-argument status of x clear, and thereby implicitly the constant status of a, b and c. In this example those constants are actually coefficient
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of an expression ; it is usually a number, but in any case does not involve any variables of the expression...

s of the polynomial, and since c occurs in a term that does not involve x, it is called the constant term of the polynomial
Constant term
In mathematics, a constant term is a term in an algebraic expression has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomialx^2 + 2x + 3,\ the 3 is a constant term....

 and can be thought of as the coefficient of x0.

Context-dependence


The context-dependent nature of the concept of "constant" can be seen in this example from elementary calculus:
since x is constant (i.e. does not depend on h) where constant means "not depending on x".

"Constant" means not depending on some variable; not changing as that variable changes. In the first case above, it means not depending on h; in the second, it means not depending on x.

See also



  • Variable
    Variable (mathematics)
    In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

  • Expression
    Expression (mathematics)
    In mathematics, an expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Symbols can designate numbers , variables, operations, functions, and other mathematical symbols, as well as punctuation, symbols of grouping, and other syntactic...

  • Mathematical constant
    Mathematical constant
    A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...

  • Physical constant
    Physical constant
    A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...


  • Constant
  • Coefficient
    Coefficient
    In mathematics, a coefficient is a multiplicative factor in some term of an expression ; it is usually a number, but in any case does not involve any variables of the expression...

  • Constant of integration
  • Constant term of a polynomial
    Constant term
    In mathematics, a constant term is a term in an algebraic expression has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomialx^2 + 2x + 3,\ the 3 is a constant term....