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)
“What is most striking in the Maine wilderness is the continuousness of the forest, with fewer open intervals or glades than you had imagined. Except the few burnt lands, the narrow intervals on the rivers, the bare tops of the high mountains, and the lakes and streams, the forest is uninterrupted.”
—Henry David Thoreau (1817–1862)
“Unless the people can choose their leaders and rulers, and can revoke their choice at intervals long enough to test their measures by results, the government will be a tyranny exercised in the interests of whatever classes or castes or mobs or cliques have this choice.”
—George Bernard Shaw (1856–1950)