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.
Read more about Real Analysis: Scope, Key Concepts
Famous quotes containing the words real and/or analysis:
“Of the three forms of pride, that is to say pride proper, vanity, and conceit, vanity is by far the most harmless, and conceit by far the most dangerous. The meaning of vanity is to think too much of our bodily advantages, whether real or unreal, over others; while the meaning of conceit is to believe we are cleverer, wiser, grander, and more important than we really are.”
—John Cowper Powys (18721963)
“Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
—Thomas Mann (18751955)