In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently.
Read more about Degree Of A Field Extension: Definition and Notation, The Multiplicativity Formula For Degrees, Examples, Generalization
Famous quotes containing the words degree of a, degree of, degree, field and/or extension:
“But in every constitution some large degree of animal vigor is necessary as material foundation for the higher qualities of the art.”
—Ralph Waldo Emerson (1803–1882)
“The world is burdened with young fogies. Old men with ossified minds are easily dealt with. But men who look young, act young and everlastingly harp on the fact that they are young, but who nevertheless think and act with a degree of caution that would be excessive in their grandfathers, are the curse of the world. Their very conservatism is secondhand, and they don’t know what they are conserving.”
—Robertson Davies (b. 1913)
“Justice in the hands of the powerful is merely a governing system like any other. Why call it justice? Let us rather call it injustice, but of a sly effective order, based entirely on cruel knowledge of the resistance of the weak, their capacity for pain, humiliation and misery. Injustice sustained at the exact degree of necessary tension to turn the cogs of the huge machine-for- the-making-of-rich-men, without bursting the boiler.”
—Georges Bernanos (1888–1948)
“How sweet I roam’d from field to field
And tasted all the summer’s pride,
Till I the Prince of Love beheld
Who in the sunny beams did glide!”
—William Blake (1757–1827)
“‘Tis the perception of the beautiful,
A fine extension of the faculties,
Platonic, universal, wonderful,
Drawn from the stars, and filtered through the skies,
Without which life would be extremely dull.”
—George Gordon Noel Byron (1788–1824)