(1) p. 22, lines 30–35 should road as follows: “immediately following any number of the set; the same is true of the numbers of a set which is dense in itself on the right only, or of a set which is dense in itself on the left only.” (Cp. p. 127, footnote ‡.)

(2) p. 38, footnote*, for XXII. read XX.

(3) pp. 55–63.

The object of the present note is to shew that there is no foundation for the doubt expressed on p. 530 of the Fortschritte der Mathematik as to the mode of treatment adopted in “The Analysis of Sets of Points” (W. H. Young, Quarterly Journal of Mathematics, 1902) for the theory of derived and deduced sets, or adherences and coherences, without the use of Cantor's numbers. The memoir quoted has to all intents and purposes been reproduced in the present volume, and in the chapter on Cantor's numbers reference is made to this theory to elucidate the matter there treated of. A synopsis of the proof of Theorem 25, Ch. IV (Theorem 7 of the memoir quoted) is appended, in which the language used is such as to shew that the use of such terms as “series of derived and deduced sets” (p. 27) and “progress a stage further” (p. 28) does not in any way require a previous knowledge of the theory of well-ordered sets or of Cantor's ordinal numbers for its comprehension or justification, and may, on the other hand, if it is desired, be entirely avoided.