| 单词 | order |
| 释义 | order (i) (Trichotomy) Precisely one of x < y, y < x, x = y holds. (ii) (Transitivity) If x < y and y < z, then x < z. (iii) If x < y, then x + z < y + z. (iv) If 0 Together with the field axioms, (i)–(iv) above, state R is an ordered field. Other examples are the rational numbers and the hyperreals. The real numbers also satisfy the completeness axiom and are the unique complete ordered field. |
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