As many mathematicians give very little thought to the theory of sets, it is perhaps worth while dwelling for moment on Dr. Sommerville's possibly misleading remarks in NATURE of October 5. He, quite correctly, points out the one-one correspondence between the aggregates of integral numbers 1, 2, 3, &c. (n), and even numbers 2, 4, 6, &c. (2n). Thus the part appears equivalent to the whole. This statement loses the character of a paradox to all who will bear in mind that the notion of the part cannot equal the whole has its origin in the contemplation of finite quantities.