Theorems · Theorem · number theory
LiouvilleNumber.remainder_lt
∀ (n : ℕ) {m : ℝ}, 2 ≤ m → LiouvilleNumber.remainder m n < 1 / (m ^ n.factorial) ^ nAn upper estimate on the remainder. This estimate works with m ∈ ℝ satisfying 2 ≤ m and is
weaker than the estimate LiouvilleNumber.remainder_lt' above. However, this estimate is
more useful for the proof.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LT.lt.trans_leproof · cited by 678
- Nat.factorialstatement · cited by 616
- one_lt_twoproof · cited by 67
- LiouvilleNumber.remainderstatement · cited by 5
- LiouvilleNumber.aux_calcproof · cited by 1
- LiouvilleNumber.remainder_lt'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- liouville_liouvilleNumberproof · cited by 1