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:
“That is the real pivot of all bourgeois consciousness in all countries: fear and hate of the instinctive, intuitional, procreative body in man or woman. But of course this fear and hate had to take on a righteous appearance, so it became moral, said that the instincts, intuitions and all the activities of the procreative body were evil, and promised a reward for their suppression. That is the great clue to bourgeois psychology: the reward business.”
—D.H. (David Herbert)
“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)