How did Georg Cantor's theory change mathematicians' understanding of infinity?

Before Georg Cantor’s work in the late 19th century, mathematicians generally assumed there was only one size of infinity. Cantor fundamentally changed this understanding by demonstrating that there are actually many different kinds of infinity, which he classified as transfinite numbers.312

Using the device of one-to-one correspondence, Cantor proved that while some infinite sets—such as the integers, rational numbers, and natural numbers—share the same size (cardinality), others are strictly larger. For instance, he showed that the set of real numbers is uncountable and therefore more numerous than the set of integers.3124

Furthermore, Cantor’s theorem established that the power set of any set is always larger than the original set, leading to an ever-increasing hierarchy of transfinite cardinalities, denoted by aleph numbers (${\aleph }_0,{\aleph }_1,{\aleph }_2,\dots$). While his revolutionary ideas initially faced significant resistance from contemporaries like Leopold Kronecker, who viewed them as overly metaphysical, Cantor’s work became foundational to modern set theory, analysis, and topology.3412