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.
> 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.
> So, in five steps I have derived the concept of number for you. There is one thing left - what happens when you can't measure a magnitude that is not a multiple of a unit and can't be expressed exactly using any part of a unit? This is called an incommensurable magnitude and the best you can do is provide an approximation such as 3.14159... or 1.414..., etc.
Others have shown quite a few problems with your construction, 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. If nothing else, all magnitudes (AB) are multiples of AB : AB, which is a unit.