In which area of mathematics does Cantor’s Theorem establish that there are different levels of infinity?

Set theory

Georg Cantor, through his groundbreaking work on set theory, overturned the mathematical understanding of infinity. His theorem proving the existence of "multiple infinities," each larger than the previous, was one of the most counterintuitive and controversial results of the time. This idea, although difficult to grasp, paved the way for a new branch of mathematics, deeply enriching our understanding of infinity and the very structure of mathematics itself. Cantor faced considerable opposition from his contemporaries, but his work is now considered foundational in the field of mathematical logic and set theory.