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This question states that π is normal:

Does Pi contain all possible number combinations?

My understanding of this is that it means that the statistically, the distribution of every number is equal across the infinite range.

If the numbering system is base π, wouldn't the number just be 1, so not normal, or does the definition only mean the bases that the number would be infinately non-repeating?

e.g π, in base π is 1 and not infinately non-repeating π in base 10 is infinately non-repeating

Let me summerise, does π base π = 1 mean that π isn't normal, or is π base π excluded from the definition because it in not infinately non-repeating?

Cheers

Dave

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    @AkivaWeinberger That also turns out to have a Wikipedia page, [here](https://en.wikipedia.org/wiki/Complex-base_system), and more generally listed under [Non-standard positional numeral systems](https://en.wikipedia.org/wiki/Non-standard_positional_numeral_systems).2016-11-17

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When we say that $x$ is normal, what we mean is that it's normal to base $b$ for every integer $b\ge2$. Base $\pi$ does not enter into the discussion.

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    Kind o$f$ like how there wo$u$ld be no p$r$ime numbers without the restriction to integer divisors...2012-11-04
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In base pi, pi is represented as 10. The same way that 10 is represented as 10 in base 10. If you are asking if pi is normal in base pi then the answer is no because it only has the digits 1 and 0 in it.

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    I suspect, Neil, that if $x$ is real and not zero, then the set of real bases to which $x$ is not normal has Lebesgue measure zero.2015-08-26