An uncountable set is a type of set that cannot be matched one-to-one with the set of natural numbers, meaning its elements are too numerous to be counted. A classic example of an uncountable set is the set of real numbers, which includes all rational and irrational numbers. This concept was introduced by mathematician Georg Cantor in the late 19th century. In contrast to countable sets, which can be listed or enumerated, uncountable sets have a greater cardinality. This means that even if you try to list all the elements of an uncountable set, there will always be more elements left unlisted. The distinction between countable and uncountable sets is fundamental in set theory, a branch of mathematical logic.