Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.
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Famous quotes containing the words real and/or analysis:
“... there is a place in the United States for the Negro. They are real American citizens, and at home. They have fought and bled and died, like men, to make this country what it is. And if they have got to suffer and die, and be lynched, and tortured, and burned at the stake, I say they are at home.”
—Amanda Berry Smith (1837–1915)
“A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.”
—Karl Marx (1818–1883)