Facts
If M/L is a field extension and L /K is another field extension, then the transcendence degree of M/K is equal to the sum of the transcendence degrees of M/L and L/K. This is proven by showing that a transcendence basis of M/K can be obtained by taking the union of a transcendence basis of M/L and one of L /K.
Read more about this topic: Transcendence Degree
Famous quotes containing the word facts:
“Get your facts first, and then you can distort them as much as you please.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“To-day ... when material prosperity and well earned ease and luxury are assured facts from a national standpoint, woman’s work and woman’s influence are needed as never before; needed to bring a heart power into this money getting, dollar-worshipping civilization; needed to bring a moral force into the utilitarian motives and interests of the time; needed to stand for God and Home and Native Land versus gain and greed and grasping selfishness.”
—Anna Julia Cooper (1859–1964)
“Had Adam tenderly reproved his wife, and endeavored to lead her to repentance instead of sharing in her guilt, I should be much more ready to accord to man that superiority which he claims; but as the facts stand disclosed by the sacred historian, it appears to me that to say the least, there was as much weakness exhibited by Adam as by Eve. They both fell from innocence, and consequently from happiness, but not from equality.”
—Sarah M. Grimke (1792–1873)