DefinitionDefinition: AI-adaptedProof: Not applicableaudited 2026-08-02

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.

Real powers for positive bases, with the zero-base positive-exponent convention

For $a > 0$ and $x \in R$ , define $a^{x} : = \exp (x \log a) .$ For the supplementary zero-base convention, define $0^{x} : = 0$ when $x > 0$ .

The expressions $0^{0}$ and $0^{x}$ for $x < 0$ are left undefined. Negative bases are not assigned arbitrary real powers.

Depends on