Use Exercise 25 to provide a proof different from that in the text that the set of rational numbers is countable. [Hint: Show that you can express a rational number as a string of digits with a slash and possibly a minus sign.]

SolutionIn this question we have to prove that set of rational numbers is countable.Step 1 Proof : Let Q be the set of rational numbers So, Q containing every rational number.At first by arranging the positive rational numbers we construct the doubly infinite array. …… ….... ….... …….Now by arranging these numbers starting from the top left hand corner,...