Theorems · Theorem · real analysis
tendsto_rpow_atTop_of_base_lt_one
∀ (b : ℝ), -1 < b → b < 1 → Filter.Tendsto (fun x => b ^ x) Filter.atTop (nhds 0)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement and proof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- Real.piproof · cited by 1,774
- Filter.univ_mem'proof · cited by 1,672
Cited by2
Results whose statement or proof uses this declaration.
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2
- AkraBazziRecurrence.tendsto_zero_sumCoeffsExpproof · cited by 1