The “proof” of Theorem A, which is purely intuitive   and logically unsatisfactory, recalls the well-known primitive   attempt to arrive at a well-ordering of a given set by successive   removal of arbitrary elements. We arrive at a correct proof only   when we start from an already well-ordered set, whose smallest   transfinite initial segment in fact has the cardinal number   ℵ0 sought. (Zermelo in Cantor 1932: 352)