DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6.1-sol)audited 2026-10-02

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Harmonic numbers for set-cover analysis

Definition

For each integer $n \geq 1$ the $n$ -th harmonic number is the finite sum $H_{n} : = \sum_{j = 1}^{n} \frac{1}{j},$ taken over the finite index set ${1, \dots, n}$ in the rational numbers. For the empty index set one sets $H_{0} : = 0$ , the empty-sum convention. Thus $H_{1} = 1$ , $H_{2} = 3 / 2$ , $H_{3} = 11 / 6$ and so on, and each $H_{n}$ is a rational number determined by the displayed finite recursion on the upper index. These are the only harmonic values used in the set-cover analysis of this page.

Used by

Weighted greedy set cover and element charges Definition
A four-element greedy set-cover charge calculation Example
Weighted greedy set cover has approximation factor Hₙ Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Williamson and Shmoys, The Design of Approximation Algorithms, §§1.1, 1.6, 2.4, 5.1–5.2, 16.2, printed pp. 14–15, 24–26, 44–46, 107–109, 413–414 (standard reference, not scraped)