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:
“I have been accustomed to make excursions to the ponds within ten miles of Concord, but latterly I have extended my excursions to the seashore.”
—Henry David Thoreau (1817–1862)
“Every boy was supposed to come into the world equipped with a father whose prime function was to be our father and show us how to be men. He can escape us, but we can never escape him. Present or absent, dead or alive, real or imagined, our father is the main man in our masculinity.”
—Frank Pittman (20th century)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)
“When all this is over, you know what I’m going to do? I’m gonna get married, gonna have about six kids. I’ll line ‘em up against the wall and tell them what it was like here in Burma. If they don’t cry, I’ll beat the hell out of ‘em.”
—Samuel Fuller, U.S. screenwriter, and Milton Sperling. Samuel Fuller. Barney, Merrill’s Marauders (1962)