On Thursday, March 6, 2014 12:16:50 AM UTC-5, John Gabriel wrote: > On Thursday, 6 March 2014 06:50:03 UTC+2, Dan Christensen wrote: > > > > > Play with words all you want, John Gabriel. > > > > It's not a case of playing with words. It's a case of well-defining every concept we use. >
No, it's playing with words.
> > > > If you want to do mathematical proofs about natural numbers, you need a list of their essential properties from which you can derive other properties. > > > > > > Wrong. You first need a well-defined method to construct those objects whose properties you wish to investigate. >
Speaking from ignorance as always.
> > > > You seem never to have written ANY mathematical proofs, or you wouldn't be saying all these stupid things. > > > > Just your ignorant assertion. >
I call 'em as I see 'em.
> > > > > You first said: > > > > 1. Peano's [axioms] defines natural numbers. > > > > And then, > > > > 2. Peano's [axioms] defines the properties of natural numbers. > > > It amounts to the same thing. What is your problem? > > > > See, there's your problem right there! Defining an object is not the same as defining its properties. Attributes define an object, not its properties. >
Says you. It makes no difference in practice.
> > > > > Nonsense. I am not about to do any such thing. A great deal of ingenuity and thought went into the construction of number. > > > > > Peano's axioms are a marvel of intellectual progress, far surpassing your hero's attempt to define numbers, significant though it was in its day and for many centuries. > > > > That's like saying Peano's rot far surpasses Euclid's definition of number. You are comparing a turd (Peano) to a mathematician (Euclid). >
What an interesting argument.
> > > > In the present day, however, his work is of no more use than slings and arrows in modern warfare. > > > > Bullshit. The Ancient Greek formulation is the only sound formulation.
Many seem to disagree. They see mostly gaping holes in your formulation, holes that even you would recognize if you ever tried to write a proof based on it.
Anyway, we seem to be going in circles here with you making the same outrageous claims over and over again. Fun as it has been kicking your butt here, it is getting a bit monotonous. If you have nothing new and relevant to add, do not expect a reply from me on this matter.