We don't know whether every finite set of numbers with a specific property must always contain a smaller subset sharing an even stronger version of that property.
open
Global / Unspecified, Global
Additive combinatorics explores these kinds of guaranteed substructure questions extensively, but many specific cases remain without a fully general proof. This continues to be an active and evolving research area.
Citation ID: WS01322
Title: We don't know whether every finite set of numbers with a specific property must always contain a smaller subset sharing an even stronger version of that property.
URL: https://worldsolve.org/index.php?api=problem&id=1322