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:
“You seem to have no real purpose in life and won’t realize at the age of twenty-two that for a man life means work, and hard work if you mean to succeed.”
—Jennie Jerome Churchill (1854–1921)
“Since time immemorial, one the dry earth, scraped to the bone, of this immeasurable country, a few men travelled ceaselessly, they owned nothing, but they served no one, free and wretched lords in a strange kingdom. Janine did not know why this idea filled her with a sadness so soft and so vast that she closed her eyes. She only knew that this kingdom, which had always been promised to her would never be her, never again, except at this moment.”
—Albert Camus 1013–1960, French-Algerian novelist, dramatist, philosopher. Janine in Algeria, in The Fall, p. 27, Gallimard (9157)
“Frankly, I’d like to see the government get out of war altogether and leave the whole field to private industry.”
—Joseph Heller (b. 1923)