According to Wikipedia, the well-ordering principle states that every set of positive integers must contain a lowest or least element. This is a very key element in validating mathematical induction as a way to prove formulas.
IMPORTANT: The goal of mathematical induction is to prove that for any number n, a given equation would find the sum of a given sequence.
The first step in mathematical induction is to prove the equation works if n=1. This is possible because of the well-ordering principle, because it proves that n=1 is possible by saying that every positive-integer set has a first number. The next step is to test for n+1, as since we know the equation applies for n=1, this would prove it applies to n=2. But in that case, since n can equal 2, it proves it for n=3, then n=4, and so on and so forth, proving the equation to be true regardless of the value of n.
Works Cited:
http://en.wikipedia.org/wiki/Well-ordering_principle
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