Irrational numbers, decimal representation

transcendental-numbers decimal-expansion number-theory irrational-numbers transcendence-theory

Can this even be proved? (Or disproved?)

Any irrational number without a 0 (zero) in its decimal representation is transcendental.

Not sure where to start on this one...


Solution 1:

Wikipedia says,

It has been conjectured that every irrational algebraic number is normal; while no counterexamples are known, there also exists no algebraic number that has been proven to be normal in any base.

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