Transcendental Numbers

Transcendental numbers are numbers that are not solutions to any algebraic equation with rational coefficients. Unlike algebraic numbers (such as ratios of integers or roots of polynomials), transcendental numbers cannot be expressed as roots of polynomial equations like \(ax^n + bx^{n-1} + \dots + c = 0\). Examples include π (pi) and e (Euler's number). They are "more complex" in a sense because they cannot be obtained through algebraic operations alone. Transcendental numbers are significant in mathematics for understanding the nature of numbers and the boundaries between algebraic and more complex, non-algebraic quantities.