x < y yields True if x is determined to be less than y. x_1 < x_2 < x_3 yields True if the x_i form a strictly increasing sequence.

x <= y or x <= y yields True if x is determined to be less than or equal to y. x_1 <= x_2 <= x_3 yields True if the x TraditionalForm\`i form a nondecreasing sequence.

x >= y or x >= y yields True if x is determined to be greater than or equal to y. x_1 >= x_2 >= x_3 yields True if the x_i form a non-increasing sequence.

SemialgebraicComponentInstances[ineqs, {x_1, x_2, ...}] gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

GenericCylindricalDecomposition[ineqs, {x_1, x_2, ...}] finds the full-dimensional part of the decomposition of the region represented by the inequalities ineqs into ...

Assumptions is an option for functions such as Simplify, Refine, and Integrate that specifies default assumptions to be made about symbolic quantities.

RegionPlot3D[pred, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}] makes a plot showing the three-dimensional region in which pred is True.