Real transcendental numbers

Real transcendental numbers are a subset of real numbers that are not algebraic. An algebraic number is defined as any number that is a root of a non-zero polynomial equation with integer coefficients. In contrast, transcendental numbers are not solutions to any such polynomial equation. For example, both rational numbers (like \( \frac{1}{2} \)) and irrational numbers (like \(\sqrt{2}\)) are algebraic, as they can be roots of polynomial equations with integer coefficients.