Theorems · Theorem · number theory
setOfPred_liouville_eq_irrational_inter_iInter_iUnion
{x | Liouville x} = {x | Irrational x} ∩ ⋂ n, ⋃ a, ⋃ b, ⋃ (_ : 1 < b), Metric.ball (↑a / ↑b) (1 / ↑b ^ n)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- Set.iUnionstatement and proof · cited by 2,483
- Set.iInterstatement and proof · cited by 1,084
- Metric.ballstatement and proof · cited by 735
- Set.inter_commproof · cited by 291
- Set.Subset.rflproof · cited by 255
- Set.Subset.antisymmproof · cited by 213
- Set.singleton_subset_iffproof · cited by 206
- Set.sdiff_subsetproof · cited by 156
- Irrationalstatement and proof · cited by 139
Cited by2
Results whose statement or proof uses this declaration.
- eventually_residual_liouvilleproof · cited by 2
- setOf_liouville_eq_irrational_inter_iInter_iUnionproof · cited by 0