Cardinality of Sets: Countable and Uncountable

This lecture covers the concept of cardinality of sets, defining countable sets as those with the same cardinality as the set of positive integers. The instructor explains how to show that a set is countable by listing its elements in a sequence. Examples include the countability of positive even integers, integers, positive rational numbers, and finite strings over a finite alphabet. The lecture also introduces the concept of uncountable sets, such as real numbers.