Theorem

Behrend's Theorem

Number Theory

Behrend's theorem is a result in arithmetic combinatorics stating that any subset of the integers from 1 to n in which no member is a multiple of any other member must have a logarithmic density that tends to zero as n grows large. The theorem is named for Felix Behrend, who published it in 1935. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts

Statement

The subsets of the integers from 1 to n in which no member of the set is a multiple of any other must have a logarithmic density that goes to zero as n becomes large. 1

Proof Year

1934 1

Classification

Statement Form

Inequality 1

Connections

Has Statement Form

Inequality

In Branch

Combinatorics

Source Behrend's theorem (Wikipedia)

Sources

1. Behrend's theorem (Wikipedia)

History
This theorem is known as Behrend's theorem because Felix Behrend proved it in 1934, and published it in 1935.
History
Felix Behrend proved it in 1934, and published it in 1935
In Branch: Combinatorics, Lead sentence
In arithmetic combinatorics, Behrend's theorem states that the subsets of the integers from 1 to n in which no member of the set i

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Behrend's Theorem

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In Branch