Theorems · Theorem · sequences and series
tendsto_inv_atTop_nhds_zero_nat
∀ {𝕜 : Type u_4} [inst : DivisionSemiring 𝕜] [inst_1 : CharZero 𝕜] [inst_2 : TopologicalSpace 𝕜] [ContinuousSMul ℚ≥0 𝕜],
Filter.Tendsto (fun n => (↑n)⁻¹) Filter.atTop (nhds 0)- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 9 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Algebra.algebraMapproof · cited by 4,706
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- ContinuousSMulstatement and proof · cited by 1,016
- CharZerostatement and proof · cited by 932
- NNRatstatement and proof · cited by 523
- DivisionSemiringstatement and proof · cited by 216
- map_natCastproof · cited by 134
Cited by9
Results whose statement or proof uses this declaration.
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- tendsto_const_div_atTop_nhds_zero_natproof · cited by 7
- tendsto_natCast_div_add_atTopproof · cited by 3
- Hyperreal.infinitesimal_epsilonproof · cited by 2
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2
- tendsto_add_mul_div_add_mul_atTop_nhdsproof · cited by 1
- EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eqproof · cited by 1
- EisensteinSeries.tendsto_zero_inv_linearproof · cited by 1
- tendsto_algebraMap_inv_atTop_nhds_zero_natproof · cited by 0