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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 !

the8thone
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2 Answers2

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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 $\sqrt{2}$.

BlackAdder
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  • Sorry, I guess I was writing as you had finished posting; I may end up deleting my post. – user99680 Jun 06 '14 at 02:18
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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 06 '14 at 03:23
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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.

user99680
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