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If $\frac{1}{\sqrt{2}}$ is representend in binary the value is $0.10110101000001...$ How can we represent the number above after inserting a zero between each digit ($0.1000101000100010000000000010$) with a formula (function)? (this formula should contain decimals constans)

EDIT: If such formula (function) doesn't exist, how to prove it?

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    Why would you think such a "formula" exists?2012-12-27
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    I will edit that. But if such formula doesn't exist. Is there a way to prove that?2012-12-27
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    What is your definition of a formula2012-12-27
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    I mean a function.2012-12-27

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