text: The zeroth law of thermodynamics describes thermal equilibrium between thermodynamic systems in form of an equivalence relation. Accordingly, all thermal systems may be divided into a quotient set, denoted as M. If the set M has the cardinality of c, then one can construct an injective function , by which every thermal system has a parameter associated with it such that when two thermal systems have the same value of that parameter, they are in thermal equilibrium. This parameter is the property of temperature. The specific way of assigning numerical values for temperature is establishing a scale of temperature. In practical terms, a temperature scale is always based on usually a single physical property of a simple thermodynamic system, called a thermometer, that defines a scaling function for mapping the temperature to the measurable thermometric parameter. Such temperature scales that are purely based on measurement are called empirical temperature scales.
  The second law of thermodynamics provides a fundamental, natural definition of thermodynamic temperature starting with a null point of absolute zero. A scale for thermodynamic temperature is established similarly to the empirical temperature scales, however, needing only one additional fixing point.