Dedekind 0.0.0
A structuralist C++23 Module Library
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dedekind::sequences::IsAbsolutelyConvergent Concept Referenceexport
module dedekind.sequences

An absolutely convergent series. Refines IsSummable: in a complete (Banach) carrier absolute convergence implies convergence, so an IsAbsolutelyConvergent witness is also IsSummable — the same refinement shape as IsConvergentSequence over IsCauchySequence. Carrier completeness is the honesty obligation that makes the implication sound; the witness opts into both traits. More...

Concept definition

template<typename Seq>
concept dedekind::sequences::IsAbsolutelyConvergent =
IsSummable<Seq> && is_absolutely_convergent_v<Seq>
dedekind::sequences::IsAbsolutelyConvergent
An absolutely convergent series. Refines IsSummable: in a complete (Banach) carrier absolute converge...
Definition convergence.cppm:282
dedekind::sequences::IsSummable
A convergent series. Necessary condition (the engineer's obligation to respect): summable ⇒ a_n → 0....
Definition convergence.cppm:266
dedekind::sequences::is_absolutely_convergent_v
constexpr bool is_absolutely_convergent_v
Opt-in: the series is absolutely convergent — the series of norms is summable.
Definition convergence.cppm:271

Detailed Description

An absolutely convergent series. Refines IsSummable: in a complete (Banach) carrier absolute convergence implies convergence, so an IsAbsolutelyConvergent witness is also IsSummable — the same refinement shape as IsConvergentSequence over IsCauchySequence. Carrier completeness is the honesty obligation that makes the implication sound; the witness opts into both traits.