One can sometimes make closure of a mathematical object by including new elements to it. The integers are a closure of the natural numbers by including negative numbers. The real numbers are a closure of the rational numbers by including square roots of positive numbers. The complex numbers are a closure of the real numbers by including square roots of negative numbers. Since every non-zero polynomial has a root in the complex numbers, the complex numbers are also the algebraic closure of the real numbers. One can express this relationship as formula_1.