To determine the set of numbers that gives the correct possible values for [tex]\( |n| \)[/tex] when [tex]\( n = 2 \)[/tex], let's start by understanding what [tex]\( |n| \)[/tex] represents. The notation [tex]\( |n| \)[/tex] refers to the absolute value of [tex]\( n \)[/tex].
The absolute value of a number is a non-negative value, which means it is always zero or positive, regardless of whether the original number is positive or negative. It represents the distance of the number from zero on the number line.
Given [tex]\( n = 2 \)[/tex]:
1. First, compute the absolute value of [tex]\( n \)[/tex]. Since 2 is already positive, [tex]\( |2| = 2 \)[/tex].
2. Now, determine the possible values. For any integer [tex]\( n \)[/tex], the possible values of [tex]\( |n| \)[/tex] are all the non-negative integers up to and including [tex]\( n \)[/tex].
Therefore, for [tex]\( n = 2 \)[/tex], the possible values of [tex]\( |n| \)[/tex] are:
[tex]\[
\{ 0, 1, 2 \}
\][/tex]
Hence, the set of numbers that gives the correct possible values for [tex]\( |n| \)[/tex] when [tex]\( n = 2 \)[/tex] is:
[tex]\[
\{ 0, 1, 2 \}
\][/tex]
So, the answer is [tex]\( 0, 1, 2 \)[/tex].
