In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers.
Read more about Real Closed Field: Definitions, Model Theory: Decidability and Quantifier Elimination, Order Properties, The Generalized Continuum Hypothesis, Examples of Real Closed Fields
Famous quotes containing the words real, closed and/or field:
“A real fox calls sour not only those grapes that he cannot reach but also those that he has reached and taken away from others.”
—Friedrich Nietzsche (1844–1900)
“Night hath closed all in her cloak,
Twinkling stars love-thoughts provoke,
Danger hence good care doth keep,
Jealousy itself doth sleep;”
—Sir Philip Sidney (1554–1586)
“The birds their quire apply; airs, vernal airs,
Breathing the smell of field and grove, attune
The trembling leaves, while universal Pan,
Knit with the Graces and the Hours in dance,
Led on th’ eternal Spring.”
—John Milton (1608–1674)