Category Archives: proof techniques

Two Fallacious Induction Arguments

Posted on September 16, 2021 by mzspivey

In this post I’m going to discuss two “proofs” by induction. That is, they’ll both be attempts at proving a statement, but they’ll both have flaws in their arguments. My hope is to alert people to potential errors when attempting … Continue reading →

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Strong Induction Wasn’t Needed After All

Posted on February 19, 2020 by mzspivey

Lately when I’ve taught the second principle of mathematical induction – also called “strong induction” – I’ve used the following example to illustrate why we need it. Prove that you can make any amount of postage of 12 cents or … Continue reading →

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The Validity of Mathematical Induction

Posted on September 21, 2017 by mzspivey

Suppose you have some statement .  Mathematical induction says that the following is sufficient to prove that is true for all natural numbers k. is true. For any natural number k, if is true, then is true. The idea is that the first … Continue reading →

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