ABSTRACT
In this definition, it is not necessary to add the other properties which are required to show that S is of the type η. For if S had a first or last term, this would be also the first or last term of M; hence we could take it away from S, and the remaining series would still satisfy the condition (2), but would have no first or last term; and the condition (2) together with (1) insures that S is a compact series. Cantor proves that any series M satisfying the above
conditions is ordinally similar to the number-continuum, i.e. the real numbers from 0 to 1, both inclusive; and hence it follows that the above definition includes precisely the same class of series as those that were included in his former definition. He does not assert that his new definition is purely ordinal, and it might be doubted, at first sight, whether it is so. Let us see for ourselves whether any extra-ordinal notions are contained in it.
