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 (the "argument") and one output (the "value of the function").:Example: If the function $f$ is defined by prescribing that $f(x)\; =\; 2x^2-3x+1$ for each real number $x$, then the input 3 will yield the function value 10 (since indeed $2cdot3^2-3cdot3+1\; =\; 10$).The function $f$ of the example is real-valued, since each and every possible function value is real. On the other hand, it is not injective, since different inputs may yield the same value; e.g., $f(-1.5)\; =\; 10$, too.

In some contexts, for convenience, functions may be considered to have several arguments and/or several values; also cf. the discussion in the article function. However, strictly seen, this is not an extension, since such functions may be considered as having single families and/or sets as input or output.

Value is also used in other senses, e.g., to specify a certain instance of a variable.:Example: $f(x)\; =\; 0$ for two separate values of $x$, namely, for $x=0.5$ and for $x=1$.

See also

*Absolute value
*Valuation (mathematics)
*Value distribution theory of holomorphic functions