On Sunday, March 2, 2014 9:46:58 AM UTC-5, John Gabriel wrote: > On Sunday, 2 March 2014 16:32:27 UTC+2, Dan Christensen wrote: > > > > On Sunday, 2 March 2014 07:06:44 UTC+2, Dan Christensen wrote: > > > > > 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." > > > > Indeed I did. :-) > > > > > 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." > > > > It's an axiom, and that's what I claimed. Nothing has changed and nothing will change. > > > > Now, you have yet to respond to my retort: > > > > Which axiom did you use to arrive at Peano's first axiom? I am asking you this to expose your folly, but you can't seem to get it. >
You are being evasive, John Gabriel. But since you ask, you don't formally "arrive at" any axioms. You just state them, and move on to deriving other statements from them -- something which, it seems, you are incapable of doing with your system of "axioms".
> > 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. > > > > I derived the entire RATIONAL NUMBERS.
You just said those were axioms! You don't formally "derive" axioms.
Again, it seems you cannot derive even the most elementary results of number theory, e.g. the existence of 2 distinct numbers (see my proof posting here)
It seems you have painted yourself into a corner, John Gabriel.