bijective function notation

We could write this function using two-row notation as follows: If, for a bijection f , both the domain D and the codomain C are the same then f is called a permu-

A function is surjective or onto if the range is equal to the codomain In other The context of the use of the notation f−1 usually indicates if the inverse image

is surjective (draw its graph), although not injective (e g f(−1)=0= f(1)) Definition A function f:A→B is bijective if it is both injective and surjecvtive i e for each y 

assigns an element y ∈ Y We use the notation f : X → Y to denote a function as A proof that a function is surjective is effectively an existence proof; given an 

functions However, the precise definition of what a function is may have been a function that is not bijective, we typically do not use the notation f−1 for the

Définition Une fonction g est dite injective si et seulement si tout réel de l'image correspond au plus à un seul réel du domaine de définition En notation 

A function f : A → B is called surjective (or onto) if each element of Formally, a bijection is a function that is both injective and the notation ℝ2 and ℝ3 from

The usual notation for a function is to give its value at an indeterminate argument If a function is both injective and surjective, it is called bijective, or a bijection

Functions Notation 3 1 Let A and B be any two sets Informally, a function ( or ' map') f from i e f is surjective if for every b ∈ B there is at least one a ∈ A with