I am recently preparing for a competitive exam and I am revising concepts again. During preparation, I mused over the following idea and got confused.
Firstly, sorry for being too verbose, and Secondly, I know my question is naive in nature. Moving from Relations to Functions, I wondered that why we required a concept of function, if we already have concept of relations. Why we require a specific type of relation in which for every single element of domain there should be a single element in co-domain? i.e. why can't co-domain have two values for single value in domain. Why we define all mathematical expressions (equations) in terms of functions?
Why we require to study a specific type of relation called function?
I know 'how' of the question i.e. How we can move from relation to function? But, I am confusion over the philosophy or mathematical requirement over the idea of Functions. Hence , I can't figure out 'why' of the question i.e. Why we require to move from relation to function to study Mathematical Function?
Final words, we study a specific relation which fulfills surjection, injection, and bi-jection, but strictly can't have two distinct values of domain having same value in co-domain. I can't image the wholesome image of requirement of function to study Mathematical Functions.