This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
 Assumptions and Domains Mathematica has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of assumptions—often in the process automatically proving a sequence of necessary mathematical theorems. Element () — specify membership in a domain (entered as Esc elem Esc) NotElement () — specify exclusion from a domain (Esc !elem Esc) Less (<), Greater (>), ... — define inequalities, implicitly for real numbers ForAll () — universal quantifier (entered as Esc fa Esc) Exists () — existential quantifier (entered as Esc ex Esc) Domains      Refine — evaluate an expression using assumptions Simplify, FullSimplify — simplify using assumptions FunctionExpand — expand in terms of simpler functions, using assumptions      Assuming — set up assumptions to be used by functions inside \$Assumptions — global default for Assumptions option      Functions Allowing Domain Specifications TUTORIALS Using Assumptions Simplifying with Assumptions Quantifiers Equations and Inequalities over Domains Complex Polynomial Systems MORE ABOUT Polynomial Systems Inequalities Logic & Boolean Algebra