DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Dedekind-infinite and Dedekind-finite sets

Definition

A set $X$ is Dedekind-infinite if some injection $f : X \to X$ is not surjective, equivalently if $X$ is equipotent with a proper subset. It is Dedekind-finite otherwise. “Infinite” alone means not bijective with a natural number; it does not include an assumption that $ω$ embeds into $X$ .

Used by

Dedekind infinitude is equivalent to a countable subset Theorem

Dependency tree · 0 levels

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

Sources

Caicedo, Some choiceless results (3), §6 definition and §8 (standard reference, not scraped)