Does taper water boil at all temperatures?

The liquid-vapor equilibrium for water in the presence of air involves a saturated liquid solution of air in water and a vapor phase composed of air and water vapor. The boiling point is the temperature at which the vapor pressure of a liquid system equals the external pressure acting on the liquid. At any temperature between the melting and boiling points of pure water, the vapor pressure of water in equilibrium with air (vapor pressure of water plus partial pressure of air) is obviously equal to the external pressure. Therefore, in an open system, such liquid solution would be at the boiling point for all temperatures at the same atmospheric pressure. However, our everyday experience does not seem to suggest it. Throughout this paper, different aspects of that apparent paradox are discussed.