Extended Real Number Line
In mathematics, the affinely extended real number system is obtained from the real number system R by adding two elements: +∞ and −∞ (read as positive infinity and negative infinity respectively). The projective extended real number system adds a single object, ∞ (infinity) and makes no distinction between "positive" or "negative" infinity. These new elements are not real numbers. It is useful in describing various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted R or .
When the meaning is clear from context, the symbol +∞ is often written simply as ∞.
Read more about Extended Real Number Line: Order and Topological Properties, Arithmetic Operations, Algebraic Properties, Miscellaneous
Famous quotes containing the words extended, real, number and/or line:
“The civility which money will purchase, is rarely extended to those who have none.”
—Charles Dickens (1812–1870)
“The modern American tourist now fills his experience with pseudo-events. He has come to expect both more strangeness and more familiarity than the world naturally offers. He has come to believe that he can have a lifetime of adventure in two weeks and all the thrills of risking his life without any real risk at all.”
—Daniel J. Boorstin (b. 1914)
“Computers are good at swift, accurate computation and at storing great masses of information. The brain, on the other hand, is not as efficient a number cruncher and its memory is often highly fallible; a basic inexactness is built into its design. The brain’s strong point is its flexibility. It is unsurpassed at making shrewd guesses and at grasping the total meaning of information presented to it.”
—Jeremy Campbell (b. 1931)
“For as the interposition of a rivulet, however small, will occasion the line of the phalanx to fluctuate, so any trifling disagreement will be the cause of seditions; but they will not so soon flow from anything else as from the disagreement between virtue and vice, and next to that between poverty and riches.”
—Aristotle (384–322 B.C.)