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based on an earlier version of the Wolfram Language.
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Inequalities
Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be solved in terms of numbers, even representing solution sets for inequalities is only made possible by Mathematica's symbolic capabilities.
Less(< ▪ Greater(> ▪ LessEqual(<= ▪ GreaterEqual(>= ▪ Equal(== ▪ Unequal(!= ▪ ...
Boole convert from inequalities to 0, 1 values
Piecewise general piecewise function

FindInstance search for particular solutions to inequalities
Reduce reduce systems of inequalities to explicit nested form

Integrate, NIntegrate integrate over regions defined by inequalities
RegionPlot, RegionPlot3D plot regions defined by inequalities
FindMinimum, NMinimize, Minimize, ... optimization over regions »

RegionFunction option for constraining 2D or 3D plots to a region
PolyhedronData find inequalities corresponding to named polyhedra

LogicalExpand expand out composite inequalities
PiecewiseExpand expand out piecewise functions
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