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 Troubles are a pigmentation in our lives here, a constant irritation that detracts from real life. But life has to do with something else as well, and it’s the other things which are the more permanent and real.”
—Brian Friel (b. 1929)
“How often should a woman be pregnant? Continually, or hardly ever? Or must there be a certain number of pregnancy anniversaries established by fashion? What do you, at the age of forty-three, have to say on the subject? Is it a fact that the laws of nature, or of the country, or of propriety, have ordained this time of life for sterility?”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“This wild night, gathering the washing as if it were flowers
animal vines twisting over the line and
slapping my face lightly, soundless merriment
in the gesticulations of shirtsleeves ...”
—Denise Levertov (b. 1923)