Why is perfect price inelasticity of demand not considered an exception to the law of demand? Assume a case of perfect price inelasticity of demand. 


 
In such a case, 


  PED = 0


The quantity demanded does not respond to changes in price, i.e. it remains constant, even when price increases or decreases (instead of falling or rising, as it should if it conformed to the inverse relation defined by the law of demand).

Thus, shouldn't perfect price inelasticity also be considered as an exception to the law of demand, just as Giffen goods and Veblen goods are?
Because although some goods have perfect inelasticity over some interval, they are not perfectly inelastic over the whole demand curve - over the rest of the curve, quantity and demand will be strictly inversely related. And the law of demand doesn't have a "strictly" in there. Price and quantity are inversely related, but not strictly so, which (in the mathematical sense) means that parts of the demand curve are allowed to be perfectly inelastic.