Most definitions of "field" I've seen include the requirement 1≠0. One book didn't, and instead defined the "characteristic" of a field as the smallest non-negative integer n such that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{k=1}^n 1=0[/tex]

The books that include the requirement 1≠0 then go on to define an "ordered field", and a "complete ordered field". ("Complete" in the sense that every set that has an upper bound has a least upper bound). Then they claim that all complete ordered fields are isomorphic. This seems to overlook the possibility that 1+1=0, or that 1+1+....+1=0 for some number of 1s on the left. Does the definition of a complete ordered field (including the axiom 1≠0) imply that the field has characteristic 0?

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# 1+1 = 0

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