mathematical proof

Strong Induction: When the Step Needs More Context

2026-06-23·3495 words·17 mins

Discrete Mathematics mathematical induction Fibonacci mathematical proof

What if the step depends on more than one earlier case, as in Fibonacci? Strong induction assumes all the earlier cases. We will see the technique at work on prime factorization, the chocolate bar, postage stamps and Binet’s formula, which in floating point fails from the 71st term on.

Mathematical Induction: Proving Properties for All Natural Numbers

2026-06-18·2762 words·14 mins

Discrete Mathematics mathematical induction logic mathematical proof

If the first domino falls and each domino knocks over the next, they all fall. That is the logic of the Principle of Mathematical Induction. We will see the structure of the proof (base case, hypothesis and step) in sums, divisibility and inequalities, and the false proof that all horses are the same color.

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