bijection of sets

Can a finite set have a bijection with a proper subset?
That means any set A can't have a bijection with a proper subset of itself since the proper subset has less elements. But every infinite set can be put in bijection with a proper subset of itself, so this is a big difference between finite sets and infinite sets which plenty of people have trouble understanding at first.
How many bijections are there from a to B?
Let's say it is sent to f. Then d can only be sent to g to have a bijection. Ok, so if b has 3 possibilities to be sent to, and c has 2 possibilities, and d has 1 possibility, then the total number of bijections from A to B are 3 × 2 × 1 = 6 (we can map the elements of A bijectively onto B in 6 different ways).
What is a bijection between two sets?
You can think of a set as a bag, which may contain no objects, finitely many objects, or even infinitely many objects. A bijection between two sets is a way to uniquely pair up objects from the two bags. By chance, are you learning about symmetric groups? As a worshipper of simplicity, I hope I've made my answer simpler than the others here so far.
What is a bijective function of a set of elements?
A bijective function of a set of elements defined to itself is called a permutation. Here every element of the set is related to itself. From the above examples of bijective function, we can observe that every element of set B has been related to a distinct element of set A.

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PDF	Lemma 027: Composition of Bijections is a Bijection Since h is both surjective (onto) and injective (1-to-1), then h is a bijection, and the sets A and C are in bijective correspondence 1Note that we have never