Intervals
Both parentheses, ( ), and square brackets, can also be used to denote an interval. The notation is used to indicate an interval from a to c that is inclusive of but exclusive of . That is, would be the set of all real numbers between 5 and 12, including 5 but not 12. The numbers may come as close as they like to 12, including 11.999 and so forth (with any finite number of 9s), but 12.0 is not included. In Europe, the notation is also used for this.
The endpoint adjoining the square bracket is known as closed, while the endpoint adjoining the parenthesis is known as open. If both types of brackets are the same, the entire interval may be referred to as closed or open as appropriate. Whenever infinity or negative infinity is used as an endpoint in the case of intervals on the real number line, it is always considered open and adjoined to a parenthesis. The endpoint can be closed when considering intervals on the extended real number line.
Read more about this topic: Bracket (mathematics)
Famous quotes containing the word intervals:
“Peter the Hermit, Calvin, and Robespierre, sons of the same soil, at intervals of three centuries were, in a political sense, the levers of Archimedes. Each in turn was an embodied idea finding its fulcrum in the interests of man.”
—Honoré De Balzac (1799–1850)
“It can be demonstrated that the child’s contact with the real world is strengthened by his periodic excursions into fantasy. It becomes easier to tolerate the frustrations of the real world and to accede to the demands of reality if one can restore himself at intervals in a world where the deepest wishes can achieve imaginary gratification.”
—Selma H. Fraiberg (20th century)
“We say that every man is entitled to be valued by his best moment. We measure our friends so. We know, they have intervals of folly, whereof we take no heed, but wait the reappearings of the genius, which are sure and beautiful.”
—Ralph Waldo Emerson (1803–1882)