The Structure of Number Systems |
Contents
THE NATURAL NUMBERS | 1 |
INTEGERS | 3 |
EXTENSIONS OF THE REAL NUMBER | 7 |
Copyright | |
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Abelian group Abelian semigroup addition and multiplication algebra associative law C₁ Cartesian product chapter Complete the proof complex numbers define definition distributive law element of G equation equivalence relation example Exercises G₁ G₂ geometry given homomorphism hypothesis integral domain isomorphic linear ordering m₁ mathematical induction mathematicians matrix multiplicative inverse n₁ n₂ natural numbers negative cut negative integer negative rational numbers number field number q number system numbers forms numbers x one-to-one correspondence ordered pairs pairs of natural points polynomials positive cuts positive integer positive rational number postulates proof is left proof of Theorem properties of addition Prove Theorem quaternions r₁ reader real numbers representative result ring S₁ S₂ set of integers set of natural set of numbers set of rational solution successor Theorem 1-9 totally ordered trichotomy law unique rational number vectors verify zero