Production will be stopped if the difference in diameter is greater than 0.002 mm.
This difference can mean that the golf ball has a diameter more than 0.002 larger than 42.67 mm, or a diameter more than 0.002 smaller than 42.67. This is the reason for using an absolute value function.
Absolute value represents the distance a number is from 0. For this function, we would want only the values where the function is less than 0.002.
kindly check the attached image below to Determine whether the given set S is a subspace of the vector space <u><em>(which is contained within a different vector space. So all the subspace is a kind of vector space in their own way, although it is also defined relative to some of the other larger vector space. The linear subspace is more often than not simply called a subspace whenever the situation serves to differentiate it from other types of subspaces.)</em></u> V.A