Theorems · Theorem · sequences and series
Real.not_summable_one_div_natCast
¬Summable fun n => 1 / ↑n
Harmonic series is not unconditionally summable.
- Defined in
- Mathlib.Analysis.PSeries
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- inv_eq_one_divproof · cited by 33
- Real.not_summable_natCast_invproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.not_summable_indicator_one_div_natCastproof · cited by 1
- Real.tendsto_sum_range_one_div_nat_succ_atTopproof · cited by 0