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.
Point-finite need not mean locally finite: intervals accumulating at the origin
Example
In , let for positive integers . The intervals are pairwise disjoint, so no point lies in two intervals and the family is point-finite. Every neighbourhood of , however, meets for all sufficiently large . Therefore the family is not locally finite at .
This shows that point-finiteness records membership at a point, whereas local finiteness controls intersections with a whole neighbourhood.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
9 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
- Locally finite collection (Wikipedia) (standard reference, not scraped)