PARTIAL FUNCTION Meaning and
Definition
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A partial function is a concept in mathematics and computer science that defines a function for only a subset of possible inputs. Unlike a total function, which is defined for all inputs within its domain, a partial function has limitations on its domain.
Formally, a partial function is defined as a relation between a set of inputs, known as the domain, and a set of outputs, known as the codomain. However, unlike a total function, which assigns a unique output value to every input in the domain, a partial function may have certain input values in the domain that do not have corresponding output values.
In other words, a partial function is a function with a restricted domain that does not cover all possible inputs. It only associates a value with inputs that are within its defined domain. For inputs outside its domain, the partial function is not defined and does not provide any output.
Partial functions are commonly used in mathematical logic, set theory, and programming languages where the possibility of undefined or missing values is desirable or inherent in the problem being solved. They allow for more flexibility in defining functions and can help handle exceptional or incomplete cases without raising errors or exceptions.
Etymology of PARTIAL FUNCTION
The word "partial function" originated from the combination of two distinct terms: "partial" and "function".
The term "partial" stems from the Latin word "partialis", which means "related to a part" or "incomplete". It was first used in English in the 15th century, referring to something that is incomplete, limited, or insufficient.
The term "function" has its roots in the Latin word "functio", which means "to perform" or "to execute". It was introduced into English in the 16th century, primarily referring to the performance of a task or a duty.
When combined, the word "partial function" forms a compound term that denotes an incomplete or limited function. In the context of mathematics and computer science, a partial function is a mathematical function that is not defined or fails to produce an output for every possible value in its domain.
