Solution set

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Solution set" – news · newspapers · books · scholar · JSTOR (January 2011) (Learn how and when to remove this message)

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

For example, for a set ${\displaystyle \{f_{i}\}}$ of polynomials over a ring ${\displaystyle R}$, the solution set is the subset of ${\displaystyle R}$ on which the polynomials all vanish (evaluate to 0), formally

${\displaystyle \{x\in R:\forall i\in I,f_{i}(x)=0\}}$

The feasible region of a constrained optimization problem is the solution set of the constraints.