The theory of progressions and of ordinal numbers, with which we have been occupied in the last chapter, is due in the main to two men—Dedekind and Cantor. Cantor’s contributions, being specially concerned with infinity, need not be considered at present; and Dedekind’s theory of irrationals is also to be postponed. It is his theory of integers of which I wish now to give an account—the theory, that is to say, which is contained in his “Was sind und was sollen die Zahlen?”* In reviewing this work, I shall not adhere strictly to Dedekind’s phraseology. He appears to have been, at the time of writing, unacquainted with symbolic logic; and although he invented as much of this subject as was relevant to his purpose, he naturally adopted phrases which were not usual, and were not always so convenient as their conventional equivalents.