Alphabeta MathHow 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.
Null rational sequences form a maximal ideal in the ring of rational Cauchy sequences
Example
Null rational sequences form a maximal ideal in the ring of rational Cauchy sequences.
Facts & Assumptions
Given: The ring of rational Cauchy sequences and its subset of null sequences.
Maximal ideals are maximal among proper ideals (Prime ideals and maximal ideals in a commutative ring).
Rational Cauchy sequences form a commutative ring (Cauchy sequences form a commutative ring).
is an ideal of (Null sequences form an ideal).
The null ideal is maximal in (The null ideal is maximal).
Verification
The ambient object is the commutative ring of [L2], and is an ideal by [L3].
The maximality statement in [L4] is precisely maximality in the ideal order of [L1].
Thus null rational sequences give a maximal ideal.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
15 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
- Tao, Analysis I (standard reference, not scraped)