Definition:Function

Definition

The process which is symbolised by an operator is called a function.

The operand(s) of the operator can be considered to be the input(s). The output of the function is whatever the operator is defined as doing with the operand(s).

A function is in fact another name for a mapping, but while the latter term is used in the general context of set theory and abstract algebra, the term function is generally reserved for mappings between sets of numbers.

When there is a need to distinguish between this and a partial function, a function is sometimes referred to as a total function.

See also

• Mapping

• Real Function
• Real-Valued Function

• Complex Function
• Complex-Valued Function

• Boolean Function
• Boolean-Valued Function

Compare partial function.

Sources

• James M. Hyslop: Infinite Series (1942): $\S 2$
• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 3.1$: Example $45$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 7.1$