>>11196126Article 1.20 is about the real number field you hideous imbecile. I am talking about
When Rudin writes, "Elements of the real number field are the real numbers," that is just an axiom which he has not proven, and that means it is only a matter of semantics. In matters of semantics, Euclid's opinion of what constitutes a real number trumps Rudin's opinion (in my opinion.) Furthermore, the properties of the real number field are given by the field axioms, and choosing to take those axioms is not preferred over my choice to take as an axiom
You can see quite plainly that in Rudin's step (4) of the proof of Article 1.19, he relies on the axioms of Definition 1.12, and if you're going to "prove" me wrong by choosing different axioms than
then you might as well argue, "By the axiom that Tooker is wrong, Tooker is wrong," and skip all your obfuscation about trying to hide behind Rudin's taking of some axioms more than 100 years after Riemann published his hypothesis.
Although in your opinion the ten or more field axioms are the best axiomatic framework to define real numbers, in my opinion the single axiom that any number which is greater than minus infinity and less than infinity is better. Since this is also the definition Euclid used, and Newton, and Cauchy, and Euler, and Gauss... I think I have more evidence that my single axiom is superior than you have that your 10 or more axioms are superior.
