Weierstrass

The Weierstrass theorem is a fundamental idea in mathematics stating that continuous functions on a closed interval can be uniformly approximated as closely as desired by polynomial functions. In simpler terms, it means any smooth curve within a certain range can be closely mimicked by a polynomial, which is like a mathematical formula composed of powers of x. This result is important because it ensures that complex continuous functions can be studied and approximated using simpler, well-understood polynomial functions, facilitating analysis, computation, and understanding of their behavior.