I know that there are countably infinite many algebraic numbers and uncountably infinite many real numbers. Therefore there exist real numbers that are not algebraic numbers. Are there any simple proofs that show certain real numbers are not algebraic?
2026-04-30 08:36:49.1777538209
Real non algebraic numbers
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Real non-algebraic numbers are called transcendental numbers. It's usually a lot harder to proof that a number is transcendental than proving that a number is algebraic. Here is an example for the number $\pi$.