This presentation was made for Truman State University's Mathematics Capstone course. We pursue a semi-rigorous proof of the Contraction Mapping on complete metric spaces and motivate it with an example of fixed-point iterative sequences. Not all of the mathematics related to this goal is shown in this presentation, so you're free to look at the paper which it is based upon.
If you'd like to delve deeper into the mathematics discussed in my presentation, look no further than the paper itself!