In 1878, Cantor had put forward the hypothesis that there is no infinite power between that of the natural numbers and the continuum. This became known as Cantor's Continuum Hypothesis (CH). With the adumbration of the number classes, CH takes on the form that the continuum has the power of the second number-class, and with the development of the aleph-scale, it assumes the form of a conjecture about the exponentiation operation in the generalised cardinal arithmetic, for it can be expressed in the form 2ℵ0 = ℵ1. The continuum problem more generally construed is really the problem of where the power of the continuum is in the scale of aleph numbers, and the generalised continuum hypothesis is the conjecture that taking the power set of an infinite set corresponds to moving up just one level in the aleph scale. For example, in 1883, Cantor had assumed (without remark) that the set of all real functions has the size of the third number-class. Given the CH, this then becomes the conjecture that 2ℵ1 = ℵ2.