NormalityOfPi.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Normality of mathematical constants

Despite extensive empirical evidence—billions of digits have been computed for $\pi$, $e$, and $\sqrt{2}$, all showing near-uniform digit distribution—it is an open problem whether any of the classical constants $\pi$, $e$, $\sqrt{2}$, $\ln 2$, or $\varphi$ is normal in any base.

References:

Imports (1)

FormalConjecturesUtil

theorem NormalNumber.pi_normal_base_ten $\pi$ is normal in base 10 sorry line 43 source
Source documentation
$\pi$ is normal in base 10.

depends on sorry what this means
Statement uses: NormalNumber.IsNormalInBase, OfNat.ofNat, Nat, Real.pi
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem pi_normal_base_ten : IsNormalInBase 10 π := by
…
```
Mentions: NormalNumber.IsNormalInBase