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:
“What might be taken for a precocious genius is the genius of childhood. When the child grows up, it disappears without a trace. It may happen that this boy will become a real painter some day, or even a great painter. But then he will have to begin everything again, from zero.”
—Pablo Picasso (1881–1973)
“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)