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:
“But real action is in silent moments. The epochs of our life are not in the visible facts of our choice of a calling, our marriage, our acquisition of an office, and the like, but in a silent thought by the way-side as we walk; in a thought which revises our entire manner of life, and says,—”Thus hast thou done, but it were better thus.””
—Ralph Waldo Emerson (1803–1882)
“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)