Well Ordering Principle

The well ordering principle states that "every non-empty subset of N has a smallest (or first) element" (http://www.proofwiki.org/wiki/Well-Ordering_Principle).

This principle is what we use during mathematical induction. The process for mathematical induction is essentially the following:
Prove that the statement is true for n = 1.
Assume that statement to be true for n + 1.
Prove that the statement is true for n + 1.
By doing this, you will prove that the statement is true for all natural numbers n.
I have found two great videos that explain the process for mathematical induction below. The first one is a bit over 9 minutes long, so I have also included a shorter video if you would not like to spend as much time watching the video.

Longer video:

Shorter video: