On 2/10/2013 3:37 AM, WM wrote: > On 9 Feb., 22:09, Virgil <vir...@ligriv.com> wrote: > >> Does the finiteness of the members of that set establish the finiteness >> of the set itself? > > The finiteness of the natural numbers in combination with the constant > difference of 1 establishes that the natural numbers are in bijection > with the initial segments. This together with principle of induction > implies that the sequence 1, 2, 3, ... has no upper threshold. It is > potentially infinite, but it is not actually infinite.
Neither yes or no.
But, one has
1) the natural numbers
2) something different from the natural numbers
This *combination* establishes a choice function for the natural numbers