What is injective and well-defined?
Could you please clarify what the concept of "injective" entails? Could you explain the difference between injective functions and non-injective ones, using a straightforward example? Furthermore, could you elaborate on the importance of well-defined functions in mathematics and their significance in finance or cryptocurrency, particularly when dealing with mappings or transformations of data? Could you possibly provide a real-world scenario where a well-defined function is crucial in either of these fields? It would be greatly appreciated if you could frame your responses in a questioning manner, so as to prompt further understanding and discussion.