On 3/11/2014 2:33 PM, John Gabriel wrote: > On Tuesday, 11 March 2014 21:09:03 UTC+2, Martin Shobe wrote: > >> The fact that you failed to construct numbers from geometry does not >> prove that Peano was an idiot. > > If I failed, that means Euclid failed. But it is well known that Euclid did not fail. :-) Therefore, we can conclude that you are an idiot? :-)
I think it's a mistake to hold mathematician from other eras to today's standards of rigor. Therefore, Euclid gets a pass, but you don't
> Of course Peano was an idiot. I proved it quite easily. You don't have natural numbers without fractions. Period.
You proved that John was an idiot quite easily, but that's setting a rather low bar.
>>>> > 3. A ratio of equal magnitudes, say AB : AB or CD : CD allows us to >>>> use either as the standard of measurement, that is, the unit. The unit >>>> is a ratio of equal magnitudes. > >>> Of course there are. They are called incommensurable magnitudes. I constructed the RATIONAL numbers. There are no other numbers. Perhaps a reread may help? :-) > >> What part is false? The part that says AB : AB is a unit? Or that AB is >> a multiple of that unit? > > If AB:AB is a unit, then AB is also a multiple of that unit. What you wrote is nonsense.
That's what I said. What you've failed to realize is that this is true for every magnitude. So every magnitude is a multiple of a unit and therefore not incommensurable.