MATH117 Lecture Notes - Lecture 37: Bijection, Identity Function, Surjective Function

• School: University of Alberta
• Department: Mathematics
• Course: MATH117
• Professor: Vladimir Troitsky

Document Summary

Math 117 - lecture 37 - terminology: inverse and restrictions. If the range is all domain (contains all possible values), it is onto. If it is both onto and one-to-one, A real function is one-to-one if the graph satisfies the horizontal line test. whenever a horizontal line meets the graph at most one point. Is onto and one to one, its a bijection. We denote the identity and we define. That is, the inverse of the inverse is the original function. A function is invertible if f is a bijection. Hence, one to one, therefore it is a bijection. Is not one to one, is one to one. From now on, let be a real function. Is monotone if it is either increasing or decreasing. similarly it is strictly monotone if it is strictly decreasing or strictly increasing. It is one to one, but clearly not monotone.