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:
“The two real political parties in America are the Winners and the Losers. The people don’t acknowledge this. They claim membership in two imaginary parties, the Republicans and the Democrats, instead.”
—Kurt Vonnegut, Jr. (b. 1922)
“We are closed in, and the key is turned
On our uncertainty;”
—William Butler Yeats (1865–1939)
“The planter, who is Man sent out into the field to gather food, is seldom cheered by any idea of the true dignity of his ministry. He sees his bushel and his cart, and nothing beyond, and sinks into the farmer, instead of Man on the farm.”
—Ralph Waldo Emerson (1803–1882)