MATH 1ZA3 Study Guide - Final Guide: Transcendentals, Mathematical Induction

• School: McMaster University
• Department: Mathematics
• Course: MATH 1ZA3
• Professor: Aaron Childs

Document Summary

A journey of a thousand miles begins with a single step . This phrase rather nicely sums up the core idea of proof by induction where we attempt to demonstrate that a property holds in an infinite, but countable, number of cases, by extrapolating from the first few. 1) the base case: our property holds for some initial case(s). 2) the induction step: show if the property holds for some nth case, it must hold for the next, the n+1 case. 3) the conclusion: once we have the first case holds, from the induction step we know if any step holds, the next step holds. So the first implies the 2nd, implies the third etc. , etc. Thus our property holds for all cases. (note: technically, this is what is known as weak induction. This differs in step 2 from the other version, called strong induction.