Wait... Is the Identity the ONLY Solution? | IMO 1977 | The Order of Mathematics | Aditya Deo Ojha скачать в хорошем качестве

Wait... Is the Identity the ONLY Solution? | IMO 1977 | The Order of Mathematics | Aditya Deo Ojha

Can you find the function? In this video, we dive deep into a legendary problem from the 1977 International Mathematical Olympiad (IMO). The Problem: Let f:N→N be a function such that f(n+1) greater than f(f(n)) for all n∈N. Determine f. This problem looks deceptively simple, but it requires a rigorous look at the properties of natural numbers. We will walk through the step-by-step proof showing why f(n)=n is the only solution that satisfies the condition. What you'll learn in this video: How to handle functional equations on the set of natural numbers. Using the Well-Ordering Principle. Mathematical Induction in Olympiad proofs. Explanation: At 14:40 we are able to say f(2) greater than 1 because we already showed that f(2) cannot be 1. Similarly when we are saying that minimum in S_k is attained at k, it is attained uniquely at k. #MathOlympiad #IMO #Mathematics #ProblemSolving #FunctionalEquations #STEM #NumberTheory #jeeadvanced