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.
> 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.
> You seem never to have written ANY mathematical proofs, or you wouldn't be saying all these stupid things.
Just your ignorant assertion.
> > 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.
> > 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).
> 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. Peano's rot is full of holes as I have shown. His "axioms" make a lot of assumptions and one can't do even the most basic arithmetic without having to define properties of addition, subtraction, etc. Peano ignores the fact that subtraction is the most primitive operator. We compare objects by difference, not by sum.
> > > To begin formally deriving number theory, however, we just list Peano's axioms at the beginning of each proof an proceed, using the rules and axioms of logic and set theory.
You are a true wanker! The Elements lasted over 2000 years and continues to last. You are trying to tell me this piece of shit (peano) surpassed that work? Well, that says to everyone you are a dolt!
What modern "academic" baboons need to do is study Euclid, not the rot of Cantor and Peano. For crying out loud, you have fools who think that (L,R) is a number. A Dedekind cut is not a number. But how would any of you know? None of you ever knew what is a magnitude, never mind a number. :-)