 Meanwhile, Cantor spent the years 1878 to 1885 publishing key works that helped turn set theory into an autonomous branch of mathematics. Let’s write \(A \equiv B\) in order to express that the two sets \(A\), \(B\) can be put in one-to-one correspondence (have the same cardinality). After proving that the irrational numbers can be put in one-to-one correspondence with \(\mathbf{R}\), and, surprisingly, that also \(\mathbf{R}^{n} \equiv \mathbf{R}\), Cantor conjectured in 1878 that any subset of \(\mathbf{R}\) would be either denumerable \((\equiv \mathbf{N})\) or \(\equiv \mathbf{R}\). This is the first and weakest form of the celebrated Continuum Hypothesis. During the following years, Cantor explored the world of point sets, introducing several important topological ideas (e.g., perfect set, closed set, isolated set), and arrived at results such as the Cantor-Bendixson theorem.