The Cardinality of Infinite Sets

The cardinality of infinite sets refers to the idea of "size" or "how many elements" a set contains, even if it's infinite. Unlike finite sets, where counting gives a clear number, infinite sets can have different sizes. For example, the set of natural numbers (1, 2, 3, ...) and the set of real numbers between 0 and 1 are both infinite, but the latter is "larger" because it has no way to pair each real number with just one natural number. Mathematicians use cardinality to compare these sizes, recognizing that some infinities are bigger than others.