real closed field

A real closed field is a special type of mathematical system that behaves like the real numbers, enabling solutions to many related problems. It includes numbers similar to real numbers, supports usual operations like addition and multiplication, and ensures every positive element has a square root. Moreover, any polynomial with coefficients in this system that can be solved over some extension can be already solved within it. Essentially, it captures properties of real numbers in a way that is complete and consistent for solving a broad class of equations, making it a fundamental concept in real algebra and geometry.