# I "Well-defined" meaning?

1. Mar 17, 2016

### HowToTrainYourDragon

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?

2. Mar 17, 2016

### Staff: Mentor

3. Mar 17, 2016

### HallsofIvy

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.