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In mathematics, a partial function from X to Y (written as f: X ↛ Y) is a function f: X ′ → Y, for some subset X ′ of X. It generalizes the concept of a function f: X → Y by not forcing f to map every element of X to an element of Y (only some subset X ′ of X). If X ′ = X, then f is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X, is not known (e.g. many functions in computability theory). Specifically, we will say that for any x ∈ X, either: * f(x) = y ∈ Y (it is defined as a single element in Y) or * f(x) is undefined.

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• Partial function
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• In mathematics, a partial function from X to Y (written as f: X ↛ Y) is a function f: X ′ → Y, for some subset X ′ of X. It generalizes the concept of a function f: X → Y by not forcing f to map every element of X to an element of Y (only some subset X ′ of X). If X ′ = X, then f is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X, is not known (e.g. many functions in computability theory). Specifically, we will say that for any x ∈ X, either: * f(x) = y ∈ Y (it is defined as a single element in Y) or * f(x) is undefined.
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