Infinite cardinality refers to the concept of measuring the size of infinite sets. Unlike finite sets, which have a specific number of elements, infinite sets can have different sizes or cardinalities. For example, the set of all natural numbers 1, 2, 3, ... is infinite, but so is the set of all real numbers x | x is a real number. However, the set of real numbers is larger than the set of natural numbers, illustrating that not all infinities are equal. The mathematician Georg Cantor developed the theory of infinite cardinality in the late 19th century. He introduced the idea of comparing different infinite sets using concepts like countable and uncountable infinities. A set is countably infinite if its elements can be matched one-to-one with the natural numbers, while an uncountably infinite set cannot be matched in this way, highlighting the complexity of infinity in mathematics.