On Sunday, March 2, 2014 2:30:06 AM UTC-5, iwa...@gmail.com wrote: > 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 arithmetic" 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.
9 hours ago, your boasted, "I gave you 100% rigorous axioms that produce ALL rational numbers.... So, in five steps I have derived the concept of number for you."
The above statement was the first of these five "steps." Now you are saying this statement wasn't derived after all, but was an "axiom" or a "definition."
So, we are back to square one. We are STILL waiting for you to derive even one result from your "axioms." Again, I suggest you try to derive the most elementary result possible from your "axioms" ALONE: that there exists a number other than 0. Forget about "common sense" or "what every 2-year-old knows." You can use only YOUR OWN "axioms", John Gabriel.