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Chapter 1: 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}. On the graph, this is represented by a circle at 2 (but not including 2), and an arrow pointing to the right (towards positive infinity), which indicates that x is greater than 2.

Step by step solution

01

Interpret the interval

The interval (2, \(\infty\)) needs to be converted into set-builder notation. The shorthand interval notation already informs us about the nature of the interval: It starts from 2 (not inclusive, denoted by the round bracket instead of square), and extends up to infinity.
02

Convert to Set-builder notation

The set-builder notation for the given interval (2, \(\infty\)) is {x | x > 2}. This read as 'the set of all x such that x is greater than 2'. The curly brackets { } denote the set, 'x' is the element of the set, the vertical bar | stands for 'such that', '>' is the symbol for 'greater than'.
03

Graph the interval on a number line

Draw a number line and put a small circle at the number 2. This circle indicates that 2 is not included in the interval. Then, draw a line pointing to the right starting from the circle to denote all numbers greater than 2 form the interval. Put an arrow at this end to indicate that the interval continues indefinitely towards positive infinity.

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