Theorems · Theorem · number theory
Liouville.transcendental
- #18 of the 100 theorems: Liouville’s Theorem and the Construction of Transcendental Numbers
∀ {x : ℝ}, Liouville x → Transcendental ℤ xLiouville's Theorem
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- mul_assocproof · cited by 1,667
- le_of_ltproof · cited by 1,175
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.mapproof · cited by 806
- Polynomial.evalproof · cited by 796
Cited by1
Results whose statement or proof uses this declaration.
- transcendental_liouvilleNumberproof · cited by 0