The discussion clarifies the distinction between a well-defined relation and a function in mathematical terms. A relation is considered well-defined if it allows for the retrieval of all corresponding values in the codomain for each element in the domain, even if multiple outputs exist for a single input. In contrast, a function is a specific type of relation where each input is mapped to exactly one output. Thus, while all functions are well-defined relations, not all well-defined relations qualify as functions.
PREREQUISITESStudents of mathematics, educators teaching algebra or calculus, and anyone interested in the foundational concepts of relations and functions.
No. That is not how "well defined" means. It means, rather, that you can get all the information required from the given definition. Yes, a "relation", as opposed to a "function" may have many "y" values corresponding to a given "x". But such a relation is "well defined" as long as it is possible to find all y corresponding to any given x.HowToTrainYourDragon said:What exactly is the difference between saying a relation is well-defined vs. saying the relation is a function? Since a relation is well-defined iff each element of the domain is mapped to exactly one element in the codomain, aren't well-defined and function basically the same thing?