Abstract
Let K be a field. An ordering of K is a subset P of K having the following properties:
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ORD 1
Given x ∊ K, we have either x ∊ P, or x = 0, or −x ∊ P, and these three possibilities are mutually exclusive. In other words, K is the disjoint union of P, {0}, and −P.
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ORD 2
If x, y ∊ P, then x + y and xy ∊ P.
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© 2002 Springer Science+Business Media New York
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Lang, S. (2002). Real Fields. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_11
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DOI: https://doi.org/10.1007/978-1-4613-0041-0_11
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