Well-Ordering Principle and Mathematical Induction

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The well ordering principle states that every non-empty set of positive integers contains a least element. Meaning that there is almost a smallest term in a set of positive integers. This principle is also equivalent to the well-ordering theorem. This includes a set of numbers, with a well-ordered subset, in which every nonempty subset contains a least element.  The whole set will depend on the framework of the natural numbers as well as the second property of numbers.  These are known as an axiom or a provable theorem.
Here's a video on the process of the well-ordering principle.

Something equivalent to the well-ordering principle is mathematical induction.  Which is what we applied in our lesson today.  Mathematical induction is basically proving how a set of numbers work, and if true, proving how it will work for any variable put in.  There are two steps to mathematical induction, and it is a bit tricky.  But once you get it, it's quite easy.

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Personally, the hardest part for me is in step two. Mostly remembering that your previous term is equal to your given, and then substituting (n+1) for n.  In addition, simplifying and verifying that both equations are equal is a bit tricky, but once you remember your factoring, it gets a lot easier!