Claims

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4 results

The study of arithmetic properties of sets: sumsets, product sets, and their expansion under addition and multiplication over the integers, reals, finite fields, and related structures. Claims about expansion estimates (e.g. the sum-product phenomenon), Freiman-type structure, and incidence methods for such questions belong here; point-configuration geometry goes to Discrete geometry, and purely D

Erdős's sum-product conjecture is false for real numbers but remains open for integers.

SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Erdős sum-product conjectureimportance · notableImportance 0.45, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The sumset of the integers with only digits 0 and 1 in base 3 and those with only digits 0 and 1 in base 4 has lower density zero.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Integers with restricted digits Logarithmic densityimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Every finite set A of integers satisfies max(|A+A|, |AA|) ≥ |A|^{2-o(1)}.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Erdős sum-product conjectureimportance · notableImportance 0.50, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

Every finite set A of real numbers satisfies max(|A+A|, |AA|) ≥ |A|^{2-o(1)}.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Erdős sum-product conjectureimportance · notableImportance 0.50, from 0 to 1 · notable: a contested point in a live debate (also the default before judging). Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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