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Real analytic function, injective, non surjective and preverving preserving the rationals ?

Hi,

I'd like to prove the none-existence non-existence of a real analytic function, injective, non-surjective that sends rationals to rationals. Is it a classical result ? If not, any hints on how to prove it ? Thanks in advance for you helpChristian Aebi.
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Real analytic function, injective, non surjective and preverving the rationals ?

Hi, I'd like to prove the none-existence of a real analytic function, injective, non-surjective that sends rationals to rationals. Is it a classical result ? If not, any hints on how to prove it ? Thanks in advance for you help Christian Aebi