The symbol for infinity is ‘‘∞,’’ and ‘‘-∞’’ is the symbol for negative infinity. These symbols mean that the numbers in the interval are getting larger in the positive or negative direction. The intervals for the previous examples and practice problems are called infinite intervals.
An interval consists of, in order, an open
parenthesis ‘‘(’’ or open bracket ‘‘[,’’ a number or ‘‘-∞,’’ a comma, a number
or ‘∞,’’ and a closing parenthesis ‘‘)’’ or closing bracket ‘‘].’’ A
parenthesis is used for strict inequalities (x < a and x > a) and a
bracket is used for an ‘‘or equal to’’ inequality (x ≤ a and x ≥ a). A
parenthesis is always used next to an infinity symbol.
Examples
Practice
Give the
interval notation for the inequality.
Solutions
The table below gives the relationship between an inequality, its region on the number line, and its interval notation.
Ordinarily the variable is written on the left in an inequality but not always. For instance to say that x is less than 3 (x < 3) is the same as saying 3 is greater than x (3 > x).
“Sumber Informasi”
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