Theorems · Theorem · real analysis
Polynomial.div_tendsto_atTop_zero_of_degree_lt
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] (P Q : Polynomial 𝕜)
[OrderTopology 𝕜],
P.degree < Q.degree → Filter.Tendsto (fun x => Polynomial.eval x P / Polynomial.eval x Q) Filter.atTop (nhds 0)- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 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.
- LinearOrderstatement and proof · cited by 8,572
- Polynomialstatement and proof · cited by 5,681
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- WithBotstatement · cited by 1,498
- OrderTopologystatement and proof · cited by 1,355
- Polynomial.natDegreeproof · cited by 1,105
- NormedFieldstatement and proof · cited by 1,084
- Polynomial.evalstatement and proof · cited by 796
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.isBigO_atTop_of_degree_leproof · cited by 2
- Polynomial.div_tendsto_atTop_zero_iff_degree_ltproof · cited by 2
- Polynomial.isLittleO_atTop_of_degree_ltproof · cited by 1
- Polynomial.div_tendsto_atBot_zero_of_degree_ltproof · cited by 1
- Polynomial.div_tendsto_zero_of_degree_ltproof · cited by 0