Properties and Facts
Finite fields cannot be ordered: in an ordered field the elements 0 < 1 < 1 + 1 < 1 + 1 + 1 < … are all different, so that an ordered field necessarily contains infinitely many elements.
Read more about this topic: Finite Field
Famous quotes containing the words properties and/or facts:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A radical is one of whom people say “He goes too far.” A conservative, on the other hand, is one who “doesn’t go far enough.” Then there is the reactionary, “one who doesn’t go at all.” All these terms are more or less objectionable, wherefore we have coined the term “progressive.” I should say that a progressive is one who insists upon recognizing new facts as they present themselves—one who adjusts legislation to these new facts.”
—Woodrow Wilson (1856–1924)