The founder of transfinite arithmetic, Georg Cantor (1845–1918), is also a founding father of set theory. He famously proved that the set of real numbers has a larger cardinal number than the set of natural numbers; the set of reals has the same cardinality as the power set (the set of all subsets) of the set of naturals. Cantor further argued that \(\aleph_0\) is the first (and smallest) transfinite cardinal number in an infinite series of increasingly larger transfinite cardinals, \(\aleph_0,\) \(\aleph_1,\) \(\aleph_2\), and so on. But note that the numerical subscripts of these alephs do n...