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The term "transcendental" itself suggests that these numbers transcend, or go beyond, algebraic numbers. This reflects their complexity and the challenges associated with categorizing them within standard mathematical frameworks. A key characteristic that adds to the complexity of transcendental numbers is the difficulty in proving that a given number is indeed transcendental.
Notable Examples
Among the most well-known transcendental numbers are ( e ) (Euler's number) and ( \pi ). These numbers have been proven transcendental, though the proofs are often intricate and not easily articulated. The effort involved in proving transcendentality contributes to the mystery and allure of these numbers.