Specializing and Generalizing Together

Abstract

Although specializing and generalizing were introduced separately, they are often hard to keep separate. The reason for specializing is to permit and to promote generalizing. Generalizations need to be checked in specific instances before looking for a convincing argument. To show how intimately they are bound together, this section begins by investigating the famous theorem of Pythagoras, which has been the starting point for many different strands of mathematics.