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:
“Whether our feet are compressed in iron shoes, our faces hidden with veils and masks; whether yoked with cows to draw the plow through its furrows, or classed with idiots, lunatics and criminals in the laws and constitutions of the State, the principle is the same; for the humiliations of the spirit are as real as the visible badges of servitude.”
—Elizabeth Cady Stanton (1815–1902)
“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)