DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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.
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AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

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Places of the rationals

Definition

A place of $Q$ is an equivalence class of nontrivial absolute values on $Q$ . By Ostrowski's theorem for the rationals, every place is represented either by the usual absolute value or by a unique $p$ -adic absolute value. We therefore write

$\infty, p$

for the archimedean place and the place represented by $∣ \cdot ∣_{p}$ .

Depends on

Ostrowski's theorem for the rationals

Used by

The product formula for the rationals Theorem
Weak approximation for rational places Theorem

Dependency tree · two levels

10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

J. S. Milne, Algebraic Number Theory, Chapter 7 (standard reference, not scraped)