How do you prove injective mapping?
Could you please elaborate on the process of proving injective mapping? I'm curious to understand the fundamental principles involved in demonstrating this mathematical concept. Could you explain the steps involved in verifying that a given mapping is indeed injective? Also, what properties should the mapping possess to qualify as injective? And if a mapping fails to be injective, how can we identify the reason for this? I'm keen to gain a deeper understanding of this topic and appreciate your assistance in clarifying these points.