Theorems · Theorem · sequences and series
isLittleO_pow_pow_of_lt_left
∀ {r₁ r₂ : ℝ}, 0 ≤ r₁ → r₁ < r₂ → (fun n => r₁ ^ n) =o[Filter.atTop] fun n => r₂ ^ n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- LE.le.transproof · cited by 3,151
- Filter.atTopstatement · cited by 2,405
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- LE.le.trans_ltproof · cited by 795
- Asymptotics.IsLittleOstatement · cited by 375
- div_nonnegproof · cited by 103
- Filter.Tendsto.congrproof · cited by 70
- div_powproof · cited by 66
- div_lt_oneproof · cited by 38
- eq_zero_of_pow_eq_zeroproof · cited by 30
Cited by5
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.isLittleO_one_of_lt_radiusproof · cited by 3
- isLittleO_pow_const_const_pow_of_one_ltproof · cited by 3
- Complex.hasSum_taylorSeries_logproof · cited by 2
- isLittleO_pow_pow_of_abs_lt_leftproof · cited by 1
- isBigO_pow_pow_of_le_leftproof · cited by 0