1. Determine whether the following functions are well defined: defined by and defined by . I would say is not well defined because, for example, , and .
2. Determine whether the function: defined by mapping a real number to the right of the decimal point in a decimal expansion of is well defined. I would say no, because while .
3. Let be a surjective map of sets. Prove that the relation is an equivalence relation whose equivalence classes are the fibers of . So basically I have to prove reflexivity, symmetry, and transitivity? How about the fibers of ?