{"paper":{"title":"Cantor set arithmetic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Bruce Reznick, Jayadev S. Athreya, Jeremy T. Tyson","submitted_at":"2017-11-23T17:59:59Z","abstract_excerpt":"Every element $u$ of $[0,1]$ can be written in the form $u=x^2y$, where $x,y$ are elements of the Cantor set $C$. In particular, every real number between zero and one is the product of three elements of the Cantor set. On the other hand the set of real numbers $v$ that can be written in the form $v=xy$ with $x$ and $y$ in $C$ is a closed subset of $[0,1]$ with Lebesgue measure strictly between $\\tfrac{17}{21}$ and $\\tfrac89$. We also describe the structure of the quotient of $C$ by itself, that is, the image of $C\\times (C \\setminus \\{0\\})$ under the function $f(x,y) = x/y$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08791","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}