Theorems · Theorem · combinatorics
isEquivalent_choose
∀ (k : ℕ), Asymptotics.IsEquivalent Filter.atTop (fun n => ↑(n.choose k)) fun n => ↑n ^ k / ↑k.factorial
n.choose k is asymptotically equivalent to n^k / k!.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Choose
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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
- Filter.atTopstatement and proof · cited by 2,405
- Nat.cast_zeroproof · cited by 1,870
- Nat.factorialstatement and proof · cited by 616
- Nat.choosestatement and proof · cited by 494
- Asymptotics.IsEquivalentstatement and proof · cited by 98
- Nat.descFactorialproof · cited by 68
- Nat.factorial_ne_zeroproof · cited by 56
- Asymptotics.IsEquivalent.reflproof · cited by 15
- Nat.cast_divproof · cited by 8
- Nat.choose_eq_descFactorial_div_factorialproof · cited by 5
- Asymptotics.IsEquivalent.divproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.tendsto_choose_mul_pow_atTopproof · cited by 1
- isTheta_chooseproof · cited by 0