Value (mathematics)
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In mathematics, value may refer to several, strongly related notions. Though in general, a mathematical value is a broad term that refers to any definite entity that can be manipulated with operators according to the well-defined rules of its mathematical system.
Certain values can correspond to the real world, although most values in mathematics generally exists purely as abstract objects with no connection to the real world.
Numerical values
[edit]Numbers (specifically the reals) are values that represent quantities. In that sense, numerical values are values that comprises or are made up of said numbers. In more simpler terms, a numerical value are represented by numbers. Both numbers and numerical values tend to be synonymous and interchangeable with each other.[1]
The following table shows certain values that are considered numerical values themselves.
| Value | Brief description |
|---|---|
| Digit value | Digit value of a place of a number would simply be its digit or numeral. |
| Place value | The contribution of a digit to the value of a number is the value of the digit multiplied by a factor of 10 raised to the power of the digit's position. |
| Ratio | How many times one number contains another. |
| Rates | The quotient of two quantites. |
| Percentage | A number or ratio expressed as a fraction of 100 |
| Central tendencies | A typical value for a probability distribution. |
Because numerical values can also be apart of composite objects, various terminologies are given. For example, a complex number , has as considered its real value, likewise as its complex value.
Variables
[edit]A variable is a symbol that represents an unspecified object. Homogeneous to numbers, variables themselves are considered as values.
Functions
[edit]The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values.[2][3]
For example, if the function f is defined by f(x) = 2x2 − 3x + 1, then assigning the value 3 to its argument x yields the function value 10, since f(3) = 2·32 − 3·3 + 1 = 10.
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
[edit]References
[edit]- ^ Collins, Joseph Victor (1893). Text-book of Algebra: Through Quadratic Equations. Albert, Scott & Company. p. 64.
- ^ "Value".
- ^ Meschkowski, Herbert (1968). Introduction to Modern Mathematics. George G. Harrap & Co. Ltd. p. 32. ISBN 0245591095.