Semialgebraic set
In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are the main object of study of real algebraic geometry the part of algebraic geometry devoted to points with real coordinates.
Tarski–Seidenberg theorem implies that the semialgebraic sets are exactly those sets that can be defined by a well-formed formula built with quantifiers , logical connectives , basic arithmetic operators , equality and inequality signs , integers, and variables representing real numbers.
