 Ever since, “set theory” has generally been identified with the branch of mathematical logic that studies transfinite sets, originating in Cantor’s result that \(\mathbf{R}\) has a greater cardinality than \(\mathbf{N}\). But, as the foregoing discussion shows, set theory was both effect and cause of the rise of modern mathematics: the traces of this origin are indelibly stamped on its axiomatic structure.