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partial function (Definition)

A function $ f:A\rightarrow B$ is sometimes called a total function, to signify that $ f(a)$ is defined for every $ a\in A$. If $ C$ is any set such that $ C\supseteq A$ then $ f$ is also a partial function from $ C$ to $ B$.

Clearly if $ f$ is a function from $ A$ to $ B$ then it is a partial function from $ A$ to $ B$, but a partial function need not be defined for every element of its domain.



"partial function" is owned by Henry.
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Also defines:  total function
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Cross-references: domain, function
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This is version 7 of partial function, born on 2002-08-23, modified 2005-05-08.
Object id is 3341, canonical name is PartialFunction.
Accessed 7080 times total.

Classification:
AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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