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interval notation - INTERVAL NOTATION When an equation is...

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INTERVAL NOTATION When an equation is solved, the solution set generally involves a finite set of numbers. For example, the solution to the equation 2 1 7 x + = is the number x = 3 , while the solutions to the equation x 2 1 10 + = are x = ± 3 . When we solve an inequality, however, the solution is usually a “connected” set of real numbers, called an interval. Using the above examples, the solutions to the inequality 2 1 7 x + > are all numbers greater than 3, and the solutions to the inequality x 2 1 10 + are all numbers between or equal to ± 3 . Interval notation provides us with some useful mathematical shorthand for representing intervals of numbers. Parentheses ( ) are used whenever the endpoint of an interval is not included in the solution set, and brackets [ ] are used whenever the endpoint is included. The symbols for positive and negative infinity, ±∞ , are used whenever an interval has only one endpoint. Brackets are never used on the infinite end of an interval involving the symbol, because infinity is a concept, not a value that a variable can ever equal. Below are some equivalent ways to represent intervals, using inequality symbols, using number lines, and using interval notation. Note that an open circle on a number line corresponds to a parenthesis in interval notation, while a closed circle corresponds with a bracket. ---------------------------------------------------------------------------------------------------------------------------------------------------------
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