A partition of a positive integer n is a way to write n as a sum of positive integers where the order of terms in the sum does not matter. For instance, 7 = 3 + 2+1 + 1 is a partition of 7. Let Pm equal the number of different partitions of m, and let Pm,n be the number of different ways to express m as the sum of positive integers not exceeding n.

a) Show that Pm,n = Pm.

b) Show that the following recursive definition for Pm,n is correct:

c) Find the number of partitions of 5 and of 6 using this recursive definition.

ECON 190 KADER WEEK 1: CHAPTER 1 Introduction to Economics I. Scarcity A. When human wants exceed resources available to satisfy them 1. Human wants are unlimited 2. Everyone struggles with scarcity B. Scarcity requires that we make choices based on available alternatives II. Economics A. The study of the...