Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30
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.

Languages over an alphabet

Definition

Let Σ be an alphabet. A language over Σ is a subset L⊆Σ∗, where Σ∗ is the set of finite words of Computation alphabets, words, the empty word, and Σ∗ and ⊆ is the subset relation of Subset x⊆y, proper subset x⊊y, and the separation notation { z∈x:φ(z) }.

Thus a language is a set of words over a fixed alphabet, not a set of alphabet symbols.

Remarks

  • The ambient alphabet matters. The same set of written strings can be viewed as a language over different alphabets only when it is contained in each corresponding Σ∗.

  • The two extreme languages over Σ are ∅ and Σ∗.

Depends on

Used by

Dependency tree · two levels

8 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