A system is said to be in thermal equilibrium when it experiences no change in its observable state (i.e. macrostate) over time. The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems.[5] In other words, the set of all equilibrated thermodynamic systems may be divided into subsets in which every system belongs to one and only one subset, and is in thermal equilibrium with every other member of that subset, and is not in thermal equilibrium with a member of any other subset. This means that a unique "tag" can be assigned to every system, and if the "tags" of two systems are the same, they are in thermal equilibrium with each other, and if they are not, they are not. Ultimately, this property is used to justify the use of thermodynamic temperature as a tagging system. Thermodynamic temperature provides further properties of thermally equilibrated systems, such as order and continuity with regard to "hotness" or "coldness", but these properties are not implied by the standard statement of the zeroth law.