theorems of existence and uniqueness

Theorems of existence and uniqueness guarantee that, for certain problems—like solving an equation or finding a specific function—there is at least one solution (existence) and that this solution is the only one (uniqueness). In practical terms, they assure us that a solution isn't just possible but also well-defined and reliably determined by the problem's conditions, providing confidence that the problem is solvable in a definitive way.