email@example.com wrote in news:firstname.lastname@example.org:
> On Sunday, March 2, 2014 9:11:22 AM UTC+2, Dan Christensen wrote: > >> > On Sunday, 2 March 2014 07:06:44 UTC+2, Dan Christensen wrote: > >> 1. A magnitude is the idea of size of extent. We can either tell that >> two > magnitudes are equal or not. If we can tell they are not equal, then > we know which is smaller or bigger, but we can't tell how much bigger > or smaller. This is called qualitative measurement (without numbers). > >> Just answer the question, John Gabriel. You listed several "axioms of >> ari > thmetic" here. Which ones in particular did you use to derive the > above statement? Did you use your 1st axiom 1? Your 2nd axiom? Which > one(s) did you use? This is not a "trick question". > > How can I use axioms if that is the first one? The words are the > definition of axiom 1. It first tells us what is a "magnitude" (the > concept of size). Then it tells us we can either determine equality or > not through qualitative measurement. The first axiom is *qualitative > measurement*. There are no numbers yet. We can only say smaller, > bigger or equal, but can't say how much smaller or how much bigger. We > can tell there is a *DIFFERENCE*. This is the most primitive operator. > Not addition and not multiplication. Look, I can derive every > arithmetical operator directly from subtraction. But I cannot do this > with any of the other operators. No, you cannot start with addition. > NEVER. > > Tell me Dannie boy, which axiom did Peano use when he wrote "0 is a > natural number" ??? > > > Difference: m-n=d > > Sum: m - (-n) = m+n > > Quotient: m/n m measured in terms of n or n measured in terms of > m. > > Reciprocal: 1/m > > Product: m*n = n / (1/m) or m / (1/n) > > As you can see, every operator is defined directly from the primitive > operator that is, subtraction.
Quotient isn't. Also is gives 3 / 6 = 2 because 6 is measured as 3 in terms of 2 (3 lots of 2)
It is only sum that is defined by you in terms of subtraction. No great trick there as long as subtraction is well defined.