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Is this true that any finite word of the alphabet $\mathcal{A_9}=\{0,1,2, \ldots,8,9\}$ appears somewhere in the decimal representation of $\sqrt{2}$ ?

Thanks !

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2 Answers 2

up vote 6 down vote accepted

What you are trying to ask is if $\sqrt{2}$ is a normal number. But while it is widely believed to be so, a proof has yet to be found.

Fun fact: Same goes for $\pi$, and that if true, everything in the universe can be expressed in the decimal digits of $\pi$ or $\sqrt{2}$.

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Sorry, I guess I was writing as you had finished posting; I may end up deleting my post. –  user99680 Jun 6 at 2:18
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Saying that $\sqrt 2$ is normal is a much stronger claim than what the8thone is asking about, though it's a very similar proposition. –  user2357112 Jun 6 at 3:23

Your question is the same, or close to, the question of whether $\sqrt 2$ is normal :http://en.wikipedia.org/wiki/Normal_number This is still open.

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No problem! Keep it and receive a +1. –  BlackAdder Jun 6 at 2:27
    
Thanks, BlackAdder. –  user99680 Jun 6 at 2:28

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