Transfinite cardinals are a type of number used in set theory to describe the sizes of infinite sets. Unlike finite numbers, which count distinct objects, transfinite cardinals help compare different infinities. For example, the set of natural numbers has a cardinality denoted by ℵ₀ (aleph-null), representing the smallest infinite size. Higher transfinite cardinals, such as ℵ₁ and ℵ₂, represent larger infinities. These cardinals arise from the work of mathematicians like Georg Cantor, who developed the concept of comparing infinite sets. Understanding transfinite cardinals is essential for exploring the foundations of mathematics and the nature of infinity.