Mapping Functions and Surjections

This lecture covers the definition of mapping functions from one set to another, focusing on surjections where every element in the codomain is the image of at least one element in the domain. Examples and properties of surjections are discussed, emphasizing the importance of surjective applications. The lecture also explores the concept of injective and surjective functions, illustrating how to show that an application is surjective using examples. Various cases are considered to demonstrate the characteristics of surjections and the uniqueness of images. The lecture concludes with a detailed analysis of bijective functions and their properties.