The first time a young student sees the mathematical constant , it
looks like just one more school artifact: one more arbitrary symbol
whose definition to memorize for the next test. Later, if he or she
persists, this perception changes. In many branches of mathematics
and with many practical applications, keeps on turning up. "There
it is again!" says the student, thus joining the ranks of
mathematicians for whom mathematics seems less like an artifact
invented and more like a natural phenomenon discovered.
So it is with regular languages. We have seen that DFAs and
NFAs have equal definitional power. It turns out that regular
expressions also have exactly that same definitional power: they can
be used to define all the regular languages, and only the regular
languages. There it is again!