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:
“We need not have the loftiest mind to understand that here is no lasting and real satisfaction, that our pleasures are only vanity, that our evils are infinite, and, lastly, that death, which threatens us every moment, must infallibly place us within a few years under the dreadful necessity of being forever either annihilated or unhappy.”
—Blaise Pascal (1623–1662)
“... 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)