On 3/11/2014 1:51 PM, John Gabriel wrote: > On Tuesday, 11 March 2014 18:35:57 UTC+2, Martin Shobe wrote: >> On 3/11/2014 10:03 AM, John Gabriel wrote: >>> In this comment, I will prove to you that Peano was an idiot once and for all.
>> You have failed spectacularly.
> On the contrary... :-)
The fact that you failed to construct numbers from geometry does not prove that Peano was an idiot.
>> > 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. > >> Others have shown quite a few problems with your construction, > > There are no errors except in your thinking. :-) > >> however I would like to point out that given your construction, there are no >> magnitudes that are not a multiple of a unit and can't be expressed >>> exactly using any part of a unit. > > Of course there are. They are called incommensurable magnitudes. I constructed the RATIONAL numbers. There are no other numbers. Perhaps a reread may help? :-) > >> If nothing else, all magnitudes (AB) are multiples of AB : AB, which is a unit. > > That is false. There are an innumerable amount of magnitudes that are not multiples of AB. I think you are confused. Try rereading.
What part is false? The part that says AB : AB is a unit? Or that AB is a multiple of that unit?