Mathematical Induction (Part 1)
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Lesson Summary:
In this lesson on Mathematical Induction (Part 1), you will discover what mathematical induction is, its origins, and how it is used to prove mathematical statements. Mathematical induction is a method of proof that allows us to prove that a mathematical proposition is valid for all natural numbers. The principle of mathematical induction is executed in just two steps, where we prove that p-suit 1 is true and assume p-suit k is true for some arbitrary k derived from here that p-suit k plus 1 is also true.
Lesson Description:
Learn what mathematical induction is, where it came from, and how it is used to prove mathematical statements.
Additional Resources:
- Mathematical Induction - An explanation of how to prove a statement by induction.
- Mathematical Induction 2 - Another extensive explanation of induction.
Questions answered by this video:
- What is mathematical induction?
- How do you use induction in math proofs?
- How can you prove the sum of odd numbers is a square using induction?
- How do you prove statements in math using induction?
- Why is the summation from k = 1 to n of 2k - 1 equal to n^2?
- Who came up with mathematical induction?
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Staff Review
This video is vital for any math major, and for many other high-level math students, such as engineering majors. Mathematical induction is usually the first major type of proof learned, and therefore, is usually confusing to those just beginning proofs. This lesson explains very well where induction comes from and how it works, but the nuts and bolts of the actual technique are a bit shaky. Make sure to check out parts 2 and 3 of this series.
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