 However, cardinal exponentiation is more powerful. It turns out to be natural to define \(2^\kappa\) as the cardinality of the power set of a set whose cardinality is \(\kappa\). (Greek letters \(\kappa\) and \(\lambda\) are traditionally used as variables to represent infinite cardinals, with letters \(\alpha\) and \(\beta\) used for ordinals.) It turns out that the cardinality of the set of real numbers (otherwise called the “continuum” for its role in representing continuous space) is the same as that of the power set of the natural numbers, \(2^{\aleph_0}\), and Cantor showed that \(2^{\aleph_0}&gt;\aleph_0\). Cantor conjectured that \(2^{\aleph_0}\) was in fact equal to \(\aleph_1\), and this conjecture was called the “Continuum hypothesis”. (See the entry on   the continuum hypothesis  for more on this conjecture and why it hasn’t been settled.)