Theorems · Theorem · sequences and series
tendsto_nat_ceil_mul_div_atTop
∀ {R : Type u_4} [inst : TopologicalSpace R] [inst_1 : Field R] [inst_2 : LinearOrder R] [IsStrictOrderedRing R]
[OrderTopology R] [inst_5 : FloorRing R] {a : R},
0 ≤ a → Filter.Tendsto (fun x => ↑⌈a * x⌉₊ / x) Filter.atTop (nhds a)- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- LE.le.transproof · cited by 3,151
- add_zeroproof · cited by 2,707
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- OrderTopologystatement and proof · cited by 1,355
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- tendsto_nat_ceil_div_atTopproof · cited by 2