ABSTRACT
Since here again we come to no greatest number, we imagine a new one, which we may call 2ω, and which is to be the first after all previous numbers ν and ω + ν.
‘The logical function which has given us the two numbers ω and 2ω is evidently different from the first principle of formation; I call it the second principle of formation of real integers, and define it more exactly as follows: If we have any determinate succession of defined real integers, among which there is no greatest number, by means of this second principle of formation a new number is created, which is regarded as the limit of those numbers, i.e. is defined as the next number greater than all of them.”
