Ich häufe ungeheure Zahlen, Gebürge Millionen auf, Ich setze Zeit auf Zeit und Welt auf Welt zu Hauf, Und wenn ich von der grausen Höh’ Mit Schwindeln wieder nach dir seh,’ Ist alle Macht der Zahl, vermehrt zu tausendmalen, Noch nicht ein Theil von dir. _Ich zieh’ sie ab, und du liegst ganz vor mir._ --HALLER, ALBR. VON. _Quoted in Hegel: Wissenschaft der Logik, Buch 1, Abschnitt 2, Kap. 2, C, b._ [Numbers upon numbers pile, Mountains millions high, Time on time and world on world amass, Then, if from the dreadful hight, alas! Dizzy-brained, I turn thee to behold, All the power of number, increased thousandfold, Not yet may match thy part. _Subtract what I will, wholly whole thou art._] =1959.= A collection of terms is infinite when it contains as parts other collections which have just as many terms in it as it has. If you can take away some of the terms of a collection, without diminishing the number of terms, then there is an infinite number of terms in the collection.--RUSSELL, BERTRAND. _International Monthly, Vol. 4 (1901), p. 93._ =1960.= An assemblage (ensemble, collection, group, manifold) of elements (things, no matter what) is infinite or finite according as it has or has not a part to which the whole is just _equivalent_ in the sense that between the elements composing that part and those composing the whole there subsists a unique and reciprocal (one-to-one) correspondence.--KEYSER, C. J. _The Axioms of Infinity; Hibbert Journal, Vol. 2 (1903-1904), p. 539._ =1961.= Whereas in former times the Infinite betrayed its presence not indeed to the faculties of Logic but only to the spiritual Imagination and Sensibility, mathematics has shown ... that the structure of Transfinite Being is open to exploration by the organon of Thought.--KEYSER, C. J. _Lectures on Science, Philosophy and Art (New York, 1908), p. 42._ =1962.= The mathematical theory of probability is a science which aims at reducing to calculation, where possible, the amount of credence due to propositions or statements, or to the occurrence of events, future or past, more especially as contingent or dependent upon other propositions or events the probability of which is known.--CROFTON, M. W. _Encyclopedia Britannica, 9th Edition; Article, “Probability.”_