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:
“I fear the popular notion of success stands in direct opposition in all points to the real and wholesome success. One adores public opinion, the other, private opinion; one, fame, the other, desert; one, feats, the other, humility; one, lucre, the other, love; one, monopoly, and the other, hospitality of mind.”
—Ralph Waldo Emerson (1803–1882)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)