Theorems · Theorem · sequences and series
HasSummableGeomSeries.summable_geometric_of_norm_lt_one
∀ {K : Type u_4} {inst : NormedRing K} [self : HasSummableGeomSeries K] (ξ : K), ‖ξ‖ < 1 → Summable fun n => ξ ^ n- Defined in
- Mathlib.Analysis.SpecificLimits.Normed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- HasSummableGeomSeries
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SummationFilter.unconditionalstatement · cited by 2,068
- NormedRingstatement and proof · cited by 924
- Summablestatement · cited by 778
- HasSummableGeomSeriesstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- summable_geometric_of_norm_lt_oneproof · cited by 13