ExistsRealQ[ineqs, {x_1, x_2, ...}] tests whether there exist real values of the x_i for which the inequalities and equations ineqs are satisfied.
ForAllRealQ[ineqs, {x_1, x_2, ...}] tests whether for all real values of the x_i the inequalities and equations ineqs are satisfied.
ImpliesRealQ[ineqs_1, ineqs_2] tests whether the inequalities and equations ineqs_1 imply the ineqs_2 for all real values of all variables.
Rules
(Mathematica Guide) Everything that Mathematica does can be thought of as derived from its ability to apply general transformation rules to arbitrary symbolic expressions. The Mathematica ...
Rules are a key part of Mathematica 's powerful expression transformation language. These "How tos" give step-by-step instructions for using rules in Mathematica .
$TimeUnit gives the minimum time interval in seconds recorded on your computer system.
n! gives the factorial of n.
The built-in functions D, Limit, Residue and Series perform computations using symbolic and analytic methods. The functions ND, NLimit, NResidue and NSeries, in this package, ...
GCD
(Built-in Mathematica Symbol) GCD[n_1, n_2, ...] gives the greatest common divisor of the n_i.