Author(s)

Dawoud Ahmadi Dastjerdi, Maryam Hosseini

Department of Mathematics, University of Guilan, Rasht, Iran.

Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture that like sets with positive upper density they have arithmetic progression of arbitrary length. Here we show their difference set may not be substantial; for any there exists such that and .

Difference Set; Density; -Set

D. Dastjerdi and M. Hosseini, "Difference Sets of Null Density Subsets of N," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 195-199. doi: 10.4236/apm.2012.23027.