On Thursday, February 27, 2014 10:39:51 PM UTC-5, John Gabriel wrote: > On Friday, 28 February 2014 01:53:27 UTC+2, Wizard-Of-Oz wrote: > > > > > > 1. The difference (or subtraction) of two numbers is that number which > > > > describes how much the larger exceeds the smaller. > > > > > So 2 - 3 = 1 > > > > Beep!! 2 < 3. Moron! Beep! Beep! >
You haven't defined - or <. I don't see them anywhere in your axioms. Is x-y = y-x?
> > > > > 3. The sum (or addition) of two numbers is that number whose difference > > > > with either of the two numbers is either of the two numbers. >
This does need a bit tweaking, to say the least.
> > Two numbers .. 2 and 3 > > > I need only consider either one or the other of those (the axiom does not > > > Lets choose 3 > > > 6 - 3 = 3 > > > That result is one of the numbers > > > So 3 + 2 = 6 >
You haven't defined +. It appears nowhere in your axioms.
> > > Beep! The difference of 6 and 2 is 4 which is not one of the numbers. Beep! Moron!!! > > > > > > 4. The quotient (or division) of two numbers is that number that measures > > > > either number in terms of the other. > > > So 2 / 6 = 3 >
Likewise, you haven't defined /. Is 2/3 = 3/2?
> > > Huh???? You sure of that? "That number" is 1/3. Moron!! Beep! Beep! > > > > > > 5. If a unit is divided by a number into parts, then each of these parts > > > > of a unit, is called the reciprocal of that number. > > > > > Lets divide the unit, 1, into 3 parts: 1/8 3/8 1/2 > > > > Beep!!!! Into "equal parts". Beep!! Moron!! >
Now you are changing your axiom. A good first step, but don't stop there.
Are you beginning to appreciate Peano's wisdom, John? Five simple, unambiguous axioms from which you can derive pretty much all of number theory. They are a thing of beauty. Take another look at them before you waste anymore time re-inventing this particular wheel.