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Chapter 6: Problem 4

Graph each set of real numbers on a number line. \(\\{x \mid x<0\\}\)

Short Answer

Expert verified
The graph would consist of an open circle at '0' with an arrow extending to the left side (negative side) of the number line, indicating the set of all real numbers less than '0'.

Step by step solution

01

Understanding the Set

The set, \(\{x \mid x<0\}\), means all numbers 'x' such that 'x' is less than 0. Simply, it includes all negative real numbers.
02

Graphing the Set on a Number Line

On a standard number line, locate the point '0'. All the values to the left (negative side) of '0' will represent the given set. To represent the 'less than' inequality, an open circle is drawn at '0' to indicate that '0' is not included in the set.
03

Finalizing the Diagram

Draw an arrow from the open circle at '0' to the left side (negative side) of the number line to represent all negative real numbers, indicating that our graph extends indefinitely to the negative side of the number line.

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