Interval Notation for Inequalities
Interval notation offers a concise mathematical way to express the solution set of an inequality. It uses a pair of endpoints separated by a comma and enclosed in specific symbols that correspond directly to their number line representation. When a boundary point is included in the solution (for or ), a square bracket or is used. When it is excluded (for or ), an open parenthesis or is used. Because solution sets of inequalities often extend infinitely in one direction, the infinity symbol represents an interval continuing endlessly to higher values, while negative infinity represents an interval extending infinitely to lower values. Since infinity and negative infinity are concepts indicating boundless continuation rather than actual numbers, they are always enclosed with an open parenthesis. Furthermore, the union symbol is used to combine intervals when the solution consists of multiple, disjoint parts of the number line. For example, the inequality is written as , is written as , and the union of two intervals like and is written as .
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