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An Axiomatic Development of the Positive integers
Models and Isomorphisms
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andy applied to lines associative law Axiom P4 Axiom Schema axiomatic theory binary operation binary relation Chapter commutative law concept Deduction Theorem applied define Definition dense ordered system element of G equation exactly x elements example Exercise extension following theorem given Hence holds induction model integral domain intuitive intuitive knowledge isomorphism Law of Addition law of logic least upper bound Lemma Let G Let x,y line 12 lines 9 logic from line mathematics multiplication nonempty notation null element null set number system object obtain one-one mapping ordered pairs Peano models positive integers proof of Theorem properties Prove Theorem rational numbers reader real numbers Right Cancellation Law Section sentence set G set H set theory solution statement Suppose symbols Theorem to lines Trichotomy Law x t G x t H x-sequence x,y e x,y t z t G