In mathematics, value may refer to several, strongly related notions.
In general, a mathematical value may be any definite
mathematical object
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a Glossary of mathematical symbols, symbol, and therefore can be involved in formulas. Commonly encounter ...
. In
elementary mathematics, this is most often a
number
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
– for example, a
real number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
such as or an
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
such as 42.
* The value of a
variable or a
constant is any number or other mathematical object assigned to it.
Physical quantities
A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a '' numerical value'' and a '' ...
have numerical values attached to units of measurement.
* The value of a
mathematical expression
In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punct ...
is the object assigned to this expression when the variables and constants in it are assigned values.
* The value of a
function, given the value(s) assigned to its
argument
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persu ...
(s), is the quantity assumed by the function for these argument values.
[
]
For example, if the function is defined by , then assigning the value 3 to its argument yields the function value 10, since .
If the variable, expression or function only assumes
real values, it is called real-valued. Likewise, a complex-valued variable, expression or function only assumes
complex values.
See also
*
Value function
*
Value (computer science)
*
Absolute value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...
*
Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...
References
{{reflist
Elementary mathematics
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