An uncountable set is a type of set that has more elements than the set of natural numbers, meaning it cannot be listed in a sequence. A classic example of an uncountable set is the set of real numbers, which includes all rational and irrational numbers. This means that no matter how you try to list them, there will always be more real numbers than you can count. The concept of uncountable sets was introduced by the mathematician Georg Cantor in the late 19th century. He demonstrated that the set of real numbers is uncountable by using a method called diagonalization. This method shows that any attempt to list all real numbers will always miss some, proving that uncountable sets are fundamentally larger than countable sets.