Mathematical Induction (Part 3)
In this lesson on mathematical induction, we learn about the stronger version of the principle called the principle of strong mathematical induction. This principle allows for the proof of propositions that may not be valid for all natural numbers. An example of a proposition that can be proved with strong induction is that any natural number greater than one is prime or the product of primes. Additionally, Fermat's method of infinite descent is introduced as a variant of the principle of mathematical induction, and it is used to prove that the square root of 2 is irrational. Finally, the well ordering principle is presented as an axiom, which is equivalent to the principle of mathematical induction.
Learn about strong mathematical induction, the well ordering principle, and Fermat's method of infinite descent. Two famous proofs are also presented.
- What is principle of strong or complete mathematical induction?
- What is Fermat's method of infinite descent?
- What is the well-ordering principle?
- How can you prove that any natural number k > 1 is either prime or the product of primes?
- How can you prove that the square root of 2 is irrational?
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Staff Review
This lesson finishes off this series of lessons with strong mathematical induction. Also discussed are Fermatâs method of infinite descent, the well ordering principle, the proof that any natural number k > 1 is either prime or the product of primes, and a very unconventional proof that the square root of 2 is irrational using the method of infinite descent. A very interesting lesson on proof.
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