12: Cardinality Last updated Save as PDF Page ID 83461 Jeremy Sylvestre University of Alberta Augustana 12.1: Finite Sets For m∈N we have defined the counting set N<m={n∈N|n<m}={0,1,…,m−1}. 12.2: Properties of finite sets and their cardinality Recall that a function f:N<n→A defines a finite sequence of elements from the set A, by setting a0=f(0),a1=f(1),a2=f(2),…,an−1=f(n−1). 12.3: Relative Sizes of Sets We have defined a set A to be finite when we can count its elements by matching them bijectively with the elements of some counting set N<m. 12.4: Counting elements of finite sets with bijections In a future chapter, we will begin learning how to count complicated collections by counting the “choices” needed to determine an arbitrary element in the collection. 12.5: Activities 12.6: Exercises