From Base Case to Infinity on Ciência Programada https://cienciaprogramada.com/series/from-base-case-to-infinity/ Recent content in From Base Case to Infinity on Ciência Programada Hugo -- gohugo.io en contato[@]cienciaprogramada.com.br (Francisco Bustamante) contato[@]cienciaprogramada.com.br (Francisco Bustamante) © 2026 Francisco Bustamante Thu, 25 Jun 2026 00:00:00 +0000 Recurrence Relations: Defining Sequences in Terms of Themselves https://cienciaprogramada.com/2026/06/recurrence-relations/ Thu, 25 Jun 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/06/recurrence-relations/ How many moves does it take to solve the Tower of Hanoi? The answer comes from a recurrence relation, which writes the problem in terms of itself with one disk fewer. We set up recurrences and solve them by substitution, by the characteristic equation and by the Master Theorem, used for merge sort. Strong Induction: When the Step Needs More Context https://cienciaprogramada.com/2026/06/strong-induction/ Tue, 23 Jun 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/06/strong-induction/ 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 https://cienciaprogramada.com/2026/06/mathematical-induction/ Thu, 18 Jun 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/06/mathematical-induction/ 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. From Base Case to Infinity: An Introduction to Induction and Recurrence https://cienciaprogramada.com/2026/06/from-base-case-to-infinity/ Wed, 17 Jun 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/06/from-base-case-to-infinity/ How do you prove a formula holds for every natural number, if there are infinitely many of them? With mathematical induction. This introduction maps out the series: classic induction, strong induction and recurrence relations, from Fibonacci to the Tower of Hanoi.