The Structure of Number Systems |
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Abelian addition algebra associative bound chapter closed commutative complete complex numbers concept Consequently Consider consists contains correspondence define definition described discussion distributive easy element equal equation equivalence relation examine example exceeds Exercises field geometry given gives greater Hence holds hypothesis identity integral domain inverse isomorphic least less linear ordering mathematicians mathematics matrix means multiplication natural numbers negative negative integer operation ordered pairs plane points positive cuts positive integer positive rational number possible postulates preserved proof proof of Theorem properties prove Prove Theorem rational numbers reader real numbers reasons relation representative requirement respect result ring S₁ satisfied semigroup set of natural solution square statement student subset successor Suppose Theorem theory true unique usual vectors verify zero