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 spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.”
—Henry Brooks Adams (1838–1918)