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Function   (English)

Definition Niveau 1

A rule for changing numbers, for example, a function might be "add one and double".

Definition Niveau 2

Something which takes in one (or more) number and turns it into another number, according to some rule.

Definition Niveau 2

A function is a special relation which exists between each member of one set and just one member(its image) in a second set.
Functions are best illustrated by mapping diagrams.
The first set in each case is often called the domain of the function, while the second set is called the co-domain and the particular images used in this second set are called the range of the function.

Definition Niveau 4

Given two sets A and B , a function f : A → B is a set f of ordered pairs (a,b) with a ∈ A and b ∈ B satisfying ∀a ∈ A( ∃(a,b) ∈ f     and (a,c) ∈ f \implies b=c) . Write f(x) for the unique element satisfying (x,f(x)) ∈ f . Compare relation.

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