From the course: Programming Foundations: Discrete Mathematics

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Prove with mathematical induction

Prove with mathematical induction

From the course: Programming Foundations: Discrete Mathematics

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Prove with mathematical induction

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- [Voiceover] One of the most important types of proof in discrete mathematics is called mathematical induction. This process allows you to verify a given theorem. Induction is the proof technique that is especially useful for proving statements about elements in a sequence. The two components of the inductive proof are first, identifying the base case, which establishes that the theorem is true for the first value in the sequence. Next, you identify the inductive step, which establishes that if the theorem is true for k, then the theorem holds true for k plus one. Therefore, if the base case is true and the inductive step is true, then the theorem holds for all natural numbers. Let's take a look at proving an identity by induction. I think mathematical induction is probably best learned by doing. So let's walk through an example. Here, I have a theorem that says for all values, n, greater than or equal to one. In other words, all positive integers. The sum of all the integers from…

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