[4][clarification needed] Cantor said: The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extra worldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical magnitude, number or order type.
In the latter two relations, where it obviously reveals itself as limited and capable for further proliferation and hence familiar to the finite, I call it Transfinitum and strongly contrast it with the absolute.
According to Cantor, Absolute Infinity is beyond mathematical comprehension and shall be interpreted in terms of negative theology.
of which one can readily convince oneself that every number γ occurring in it is the type [i.e., order-type] of the sequence of all its preceding elements (including 0).
Although Zermelo's fix allows a class to describe arbitrary (possibly "large") entities, these predicates of the metalanguage may have no formal existence (i.e., as a set) within the theory.
nach drei Beziehungen unterschieden: erstens, sofern es in der höchsten Vollkommenheit, im völlig unabhängigen außerweltlichen Sein, in Deo realisiert ist, wo ich es Absolut Unendliches oder kurzweg Absolutes nenne; zweitens, sofern es in der abhängigen, kreatürlichen Welt vertreten ist; drittens, sofern es als mathematische Größe, Zahl oder Ordnungstypus vom Denken in abstracto aufgefaßt werden kann.
In den beiden letzten Beziehungen, wo es offenbar als beschränktes, noch weiterer Vermehrung fähiges und insofern dem Endlichen verwandtes A.-U.