The documentation for the computer language Java recommends that when an equals method

Chapter 8, Problem 34

(choose chapter or problem)

The documentation for the computer language Java recommends that when an “equals method” is defined for an object, it be an equivalence relation. That is, if R is defined as follows:

x R y \(\Leftrightarrow\) x.equals(y) for all objects in the class,

then R should be an equivalence relation. Suppose that in trying to optimize some of the mathematics of a graphics application, a programmer creates an object called a point, consisting of two coordinates in the plane. The programmer defines an equals method as follows: If p and q are any points, then

p.equals(q) \(\Leftrightarrow\) the distance from p to q is less than or equal to c

where c is a small positive number that depends on the resolution of the computer display. Is the programmer’s equals method an equivalence relation? Justify your answer.

Text Transcription:

Leftrightarrow