DictionaryThesaurusScrabbleExamplesQuiz

ordered field meaning

EN
WOrdered field
  • In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
  • An ordered field necessarily has characteristic 0, all natural numbers, i.e. the elements 0, 1, 1 + 1, 1 + 1 + 1, … are distinct. This implies that an ordered field necessarily contains an infinite number of elements: a finite field cannot be ordered.
  • Every subfield of an ordered field is also an ordered field in the inherited order. Every ordered field contains an ordered subfield that is isomorphic to the rational numbers. Any Dedekind-complete ordered field is isomorphic to the real numbers.
ordered field
ordered field
  • Part-of-Speech Hierarchy
    1. Nouns
      • Countable nouns
    Source: Wiktionary
     0 0

    Meaning of ordered field for the defined word.

    Grammatically, this idiom "ordered field" is a noun, more specifically, a countable noun.
    Definiteness: Level 1
    12345678910
    Definite    ➨     Versatile
    0.076