Theorems · Theorem · sequences and series
tendsto_pow_atTop_nhds_zero_iff
∀ {𝕜 : Type u_4} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [Archimedean 𝕜]
[inst_4 : TopologicalSpace 𝕜] [OrderTopology 𝕜] {r : 𝕜},
Filter.Tendsto (fun n => r ^ n) Filter.atTop (nhds 0) ↔ |r| < 1- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- 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
- absstatement and proof · cited by 1,814
- OrderTopologystatement and proof · cited by 1,355
- le_of_ltproof · cited by 1,175
- Archimedeanstatement and proof · cited by 603
- one_powproof · cited by 521
Cited by2
Results whose statement or proof uses this declaration.
- tendsto_pow_atTop_nhds_zero_iff_norm_lt_oneproof · cited by 3
- NNReal.tendsto_pow_atTop_nhds_zero_iffproof · cited by 1