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:
“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”
—Thomas Jefferson (1743–1826)
“The real history of consciousness starts with one’s first lie.”
—Joseph Brodsky (b. 1940)
“Strange goings on! Jones did it slowly, deliberately, in the bathroom, with a knife, at midnight. What he did was butter a piece of toast. We are too familiar with the language of action to notice at first an anomaly: the ‘it’ of ‘Jones did it slowly, deliberately,...’ seems to refer to some entity, presumably an action, that is then characterized in a number of ways.”
—Donald Davidson (b. 1917)
“Our first line of defense in raising children with values is modeling good behavior ourselves. This is critical. How will our kids learn tolerance for others if our hearts are filled with hate? Learn compassion if we are indifferent? Perceive academics as important if soccer practice is a higher priority than homework?”
—Fred G. Gosman (20th century)