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单词 BeattysTheorem
释义

Beatty’s theorem


If p and q are positive irrationals such that

1p+1q=1

then the sequences

{np}n=1=p,2p,3p,
{nq}n=1=q,2q,3q,

where x denotes the floor (or greatest integer function) of x, constitute a partitionMathworldPlanetmathPlanetmath of the set of positive integers.

That is, every positive integer is a member exactly once of one of the two sequences and the two sequences have no common terms.

TitleBeatty’s theorem
Canonical nameBeattysTheorem
Date of creation2013-03-22 11:56:34
Last modified on2013-03-22 11:56:34
Ownerdrini (3)
Last modified bydrini (3)
Numerical id6
Authordrini (3)
Entry typeTheorem
Classificationmsc 11B83
Related topicSequence
Related topicIrrational
Related topicPartition
Related topicFloor
Related topicCeiling
Related topicBeattySequence
Related topicFraenkelsPartitionTheorem
Related topicFraenkelsPartitionTheorem2
Related topicConjugateIndex
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更新时间:2025/5/4 21:35:12