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Field Axioms

  1. Mar 24, 2012 #1
    Hi there,

    In most books that I saw, the set of real numbers under the usual sum and product is considered as a Field and say that's by the field axioms. But I have surprised when I have seen, it is a theorem. The question, are these axioms? or can they be proved?

    Thank you very much.
     
  2. jcsd
  3. Mar 24, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    What are "axioms" and what are "theorems" depends upon what level you are working at.

    We define a field to be a set of objects, S, together with two binary operations, + and *, satisfying the "field axioms".

    We can the prove, as a theorem, that a particular set, with given binary operations, such as the rational numbers or real numbers, satisfy those axioms.
     
  4. Mar 24, 2012 #3
    Thank you
     
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