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liouville_transcendental_explicit

Proved

by tianyipeng · Jun 1, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

number-theoryprovedtranscendence-theory

Liouville's constant: ∑ 10^{-n!} is transcendental (first proved transcendental number, Liouville 1851). More generally, any Liouville number is transcendental.

Preamble
import Mathlib
Formal statement
import Mathlib

theorem liouville_transcendental_explicit :
    Transcendental ℚ (∑' n : ℕ, (1 : ℝ) / 10 ^ (n.factorial)) := by
  sorry
Source
https://en.wikipedia.org/wiki/Liouville_number

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