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Chapter 0: Problem 7

Express each interval in set-builder notation and graph the interval on a number line. $$(2, \infty)$$

Short Answer

Expert verified
The set-builder notation for the interval (2, \( \infty \)) is {x | x > 2}. In the graphic representation on a number line, an open circle is drawn at 2 with a line pointing to the right, indicating that all numbers greater than 2 are included in the set.

Step by step solution

01

Convert the Interval to Set-Builder Notation

Set-builder notation is an efficient way to describe sets. It uses a variable, followed by a vertical line (or colon), and a condition that elements must satisfy. The given interval can be written in set-builder notation as {x | x > 2}. This set includes all real numbers 'x' greater than 2.
02

Draw the Number Line

Draw a straight, horizontal line to represent a number line. Mark a point for the number 2.
03

Graph the Interval on the Number Line

Since the interval (2, \( \infty \)) does not include the number 2, a small open circle is drawn at 2. Draw a line pointing to the right of 2 to indicate that the set includes all numbers greater than 2 to \( \infty \).

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