We discuss the strategy of determining properties of many-body systems by applying successively more stringent limitations on the domain on which solutions can lie, i.e., sharpening the degree of resolution of the results obtained. A rough division is made into universal, or system-independent inequalities and system-dependent ones, which are joined by equalities or sum rules. General examples include Fermion ground states and classical fluids in thermal equilibrium, and for the latter, the effect of estimation by saturating inequalities. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
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