Prove that every ordered field has no smallest positive element.
An ordered field has no smallest positive element
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$\begingroup$
ordered-fields
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1 Answers
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Hint: Suppose that $x$ is the smallest positive element. Show that $1/2$ is positive, and thus $x/2$ is positive. Thus $0
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1@waltermiller: $1$ must be positive, since $1=1^2$; since $1$ is positive, $1+1$ is positive. Since $1+1$ is positive, $\frac{1}{1+1}$ is positive. – 2012-05-08