On 31 Mai, 16:56, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > I see.
No, you don't. You intermingle mathematical theorems and logical foundations. Mathematical theorems can be proven using axioms and logic.
Logical foundations cannot be proven (how should they? By some pre- logic laws?). Logical foundations can only be obtained from observing the behaviour of sets --- necessarily finite sets, because there are no infinite sets in reality that could be observed.
This observation results in a logical law that states: Every linear complete set has a last element.
Think a while about that. Then you may come back and tell us the result (not about the truth of what I just said, but about your level of having understood it).