Definition
A Banach space is a vector space X over the field of real numbers R or complex numbers C which is equipped with a norm and which is complete with respect to that norm. Formally, the definition of a Banach space is :
- A normed space X is said to be a Banach space if for every Cauchy sequence there exists an element x in X such that .
Read more about this topic: Banach Space
Famous quotes containing the word definition:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)