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.
The pole of zeta at recovers Euclid's infinitude of primes without reminting it on this page
The existing arithmetic theorem Euclid's theorem: for every and every list of primes there is a prime not among ; consequently the set of primes is not finite already proves that there are infinitely many primes. The Euler product The Riemann zeta function has its Euler product on the half-plane shows why the zeta function sees the same fact: once the later continuation theorem on this page identifies a simple pole at , the product cannot be a finite product, so it encodes a second proof of infinitude. This page records that agreement but does not duplicate the arithmetic theorem under a new complex-analysis id.
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Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
30 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
- Elias M. Stein and Rami Shakarchi, Complex Analysis, Ch. 6 §2 (standard reference, not scraped)
- K. Chandrasekharan, Lectures on the Riemann Zeta-Function, Lecture 11 §3 (standard reference, not scraped)