Algebraic Closure

Algebraic closure refers to the idea that for any given set of numbers (like real numbers), there exists a larger set in which every polynomial equation can be solved. Specifically, in the context of mathematics, the algebraic closure of a field (like the rational numbers) includes solutions to all polynomial equations with coefficients from that field. For example, the algebraic closure of the real numbers is the complex numbers, where every polynomial equation with real coefficients has a solution. This concept ensures that we can always find roots for equations within an extended mathematical framework.