Table of Contents
Learn Bijective Function on Infinity Learn
A bijective function is a function that is both injective and surjective. This means that it maps every element in its domain to a unique element in its range, and that it also maps every element in its range back to its original element in the domain.
Surjective, Injective and Bijective Functions
A function is said to be surjective if for every element in the codomain there exists at least one element in the domain such that the function maps that element to the codomain element.
A function is said to be injective if for every element in the domain there exists at most one element in the codomain such that the function maps that element to the codomain element.
A function is said to be bijective if it is both surjective and injective.
Bijective Function Definition
A bijective function is a function that is both injective and surjective.
Bijective Function Properties
A bijective function is a function that is both injective and surjective.
How to prove that a Function is Bijective?
There are a few steps in proving that a function is bijective. The first is to show that the function is injective, meaning that every element in the domain of the function is mapped to a unique element in the range of the function. The second step is to show that the function is surjective, meaning that every element in the range of the function is mapped to an element in the domain of the function. The third and final step is to show that the function is bijective, meaning that the function is both injective and surjective.
Important Points to Remember for Bijective Function:
A bijective function is a function that is both injective and surjective.
A bijective function can be represented by a bijection diagram, which will show the function’s inputs and outputs.
A bijection diagram will always be a one-to-one correspondence.
