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A relation that is functional and total. For example, the red and green relations in the diagram are functions, but the blue and black ones are not. An injection [d] A function that is injective. For example, the green relation in the diagram is an injection, but the red, blue and black ones are not. A surjection [d] A function that is surjective.
Such functions appear in the same column of the table above. Likewise, the functions f and g are R-related if and only if f(x) = f(y) ⇔ g(x) = g(y) for x and y in {1, 2, 3}; such functions are in the same table row. Consequently, two functions are D-related if and only if their images are the same size. The elements in bold are the idempotents.
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given by (a, c) ∈ S o R ⇔ for some b ∈ B, (a, b) ∈ R and (b, c) ∈ ...
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
Russell defines functions of propositions with arguments, and truth-functions f(p). [62] For example, suppose one were to form the "function of propositions with arguments" p 1: "NOT(p) AND q" and assign its variables the values of p: "Bob is hurt" and q: "This bird is hurt".
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Functional programming is the programming paradigm consisting of building programs by using only subroutines that behave like mathematical functions. For example, if_then_else is a function that takes three functions as arguments, and, depending on the result of the first function (true or false), returns the result of either the second or the ...
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