Theorems · Theorem · sequences and series
tendsto_pow_atTop_nhds_zero_iff_norm_lt_one
∀ {R : Type u_2} [inst : SeminormedRing R] [NormMulClass R] {x : R},
Filter.Tendsto (fun n => x ^ n) Filter.atTop (nhds 0) ↔ ‖x‖ < 1- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingNormMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- pow_oneproof · cited by 894
- norm_nonnegproof · cited by 725
- SeminormedRingstatement and proof · cited by 446
- pow_succproof · cited by 374
- abs_of_nonnegproof · cited by 279
Cited by3
Results whose statement or proof uses this declaration.
- AbsoluteValue.isEquiv_iff_isHomeomorphproof · cited by 0
- Complex.UnitDisc.tendsto_pow_atTop_nhds_zeroproof · cited by 0
- PadicInt.continuousAddCharEquiv_of_norm_mul_symm_applystatement · cited by 0