CMPSC 40 Lecture Notes - Lecture 10: Mathematical Induction, Bijection, Arithmetic Progression
Document Summary
A function from to , denoted is an assignment of each element of to exactly one element of. A function can alsob e defined as a relation, a subset of the cartesian product. , where no two elements of the relation have the same first element. At most one arrow going into each element in. Each element in is the image of at most one element of under. At least one arrow going into each element in. Each element in is the image of at least one element of under. Exactly one arrow going into each element in. Each element in is the image of exactly one element of. The composition of with (or of and ), denoted. , is the function from to defined by. For this to work, the range of must be a subset of the domain of. Let be a function from the set to the set .
