# Is π normal in base π?

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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What does base $\pi$ mean after all? Usually one talks about bases $b$ only if $b$ is an integer $\ge 2$. – Hagen von Eitzen Oct 19 '12 at 14:58
You have to define what it means to be in a base that is not an integer. In particular, with integer base, "almost" every real number is uniquely represented in the base. I'm not sure this is true for non-integer bases. – Thomas Andrews Oct 19 '12 at 15:00

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.
Careful --- I didn't say "bases can only be integers" --- I said that when it comes to deciding whether something is normal bases can only be integers. The reason for this is clear; if you don't restrict the bases, there aren't any normal numbers, since no number $x$ is normal to base $x$. Bases don't have to be integers, and there are many papers devoted to the properties of expansions to non-integer bases. It's just in the context of normality that we can't get anywhere without the restriction. – Gerry Myerson Oct 21 '12 at 22:51