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:
“No: until I want the protection of Massachusetts to be extended to me in some distant Southern port, where my liberty is endangered, or until I am bent solely on building up an estate at home by peaceful enterprise, I can afford to refuse allegiance to Massachusetts, and her right to my property and life. It costs me less in every sense to incur the penalty of disobedience to the State than it would to obey. I should feel as if I were worth less in that case.”
—Henry David Thoreau (1817–1862)
“Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a classical front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.”
—Eric Gill (1882–1940)
“Again, the great number of cultivated men keep each other up to a high standard. The habit of meeting well-read and knowing men teaches the art of omission and selection.”
—Ralph Waldo Emerson (1803–1882)
“There’s a line between love and fascination that’s hard to see on an evening such as this.”
—Ned Washington (1901–1976)