What makes something injective?
Could you please elaborate on what precisely qualifies something as being injective? Could you provide an example or two to illustrate the concept? Furthermore, how does the property of injectivity differ from other related mathematical properties like surjectivity or bijectivity? Also, in what contexts is the concept of injectivity particularly important or useful? Finally, are there any common misconceptions or pitfalls that beginners often encounter when trying to grasp the idea of injectivity?