[PDF] BIJECTIVE PROOF PROBLEMS 18 авг. 2009 г. 16. Page 17.

When is a function bijective?

Recall: A bijection is a function that is both injective and surjctive. We also showed that a function is bijective if and only if it is invertible. Example 1: The sets Z •1 and Z •1

How many bijective functions are there in a set?

So there are 6 ordered pairs i.e. 6 bijective functions which is equivalent to (3!). So as we see that in the set A there are 3 elements so the total bijective functions to itself are (3!). Now if there are n elements in any set so the number of ordered pairs are (n!). So, the number of bijective functions to itself are (n!).

What is a bijection in math?

Recall: A bijection is a function that is both injective and surjctive. We also showed that a function is bijective if and only if it is invertible. Example 1: The sets Z •1 and Z •1 have the same cardinality since f : Z •1 Ñ Z •1 x ?Ñ x is a bijective map. Example 2: The sets Z •´2 and Z •1 have the same cardinality since f : Z •´2 Ñ Z •1

How do you know if a function is a bijection?

A function is a bijection if it is both injective and surjective. Every element in A has a unique image in the codomain and every element of the codomain has a pre-image in the domain. Discover the wonders of Math! Example 1: Prove that the one-one function f : {1, 2, 3} ? {4, 5, 6} is a bijective function.