Price Elasticity at Terminal Points

The price elasticity at terminal point N equals 0 means that at point N, e = 0. At terminal point M, although, price-elasticity is undefined, however most texts show that at terminal point M, e = ∞. According to William J. Baumol, a Nobel Prize winner, price elasticity at upper terminal point of the demand curve is undefined. It is undefined since measuring elasticity at terminal point (M) includes division of zero and division by-zero is undefined. In his own words, 'Here elasticity isn't even defined since an attempt to evaluate thefraction p/x at that point forces us to commit the sign of dividing by zero. The reader who has forgotten why division by zero is immoral can recall that division is the reverse operation of multiplication. Since in seeking the quotient c = a/b we look for a number, c that when multiplied by b gives us the number a, which is, for which cb = a. But if a isn't zero, say a = 5 and b is zero, there isno such number since there is no c such that c x 0 = 5".