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:
“I think the Senate ought to realize that I have to have about me those in whom I have confidence; and unless they find a real blemish on a man, I do not think they ought to make partisan politics out of appointments to the Cabinet.”
—Calvin Coolidge (1872–1933)
“With two sons born eighteen months apart, I operated mainly on automatic pilot through the ceaseless activity of their early childhood. I remember opening the refrigerator late one night and finding a roll of aluminum foil next to a pair of small red tennies. Certain that I was responsible for the refrigerated shoes, I quickly closed the door and ran upstairs to make sure I had put the babies in their cribs instead of the linen closet.”
—Mary Kay Blakely (20th century)
“Something told the wild geese
It was time to go.
Though the fields lay golden
Something whispered—”Snow.””
—Rachel Lyman Field (1894–1942)