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:
“When much intercourse with a friend has supplied us with a standard of excellence, and has increased our respect for the resources of God who thus sends a real person to outgo our ideal; when he has, moreover, become an object of thought, and, whilst his character retains all its unconscious effect, is converted in the mind into solid and sweet wisdom,—it is a sign to us that his office is closing, and he is commonly withdrawn from our sight in a short time.”
—Ralph Waldo Emerson (1803–1882)
“... the big courageous acts of life are those one never hears of and only suspects from having been through like experience. It takes real courage to do battle in the unspectacular task. We always listen for the applause of our co-workers. He is courageous who plods on, unlettered and unknown.... In the last analysis it is this courage, developing between man and his limitations, that brings success.”
—Alice Foote MacDougall (1867–1945)