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Addition of Sequences: Study of Density Relationships

In: Sequences

Author

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  • H. Halberstam

    (University of Illinois, Department of Mathematics)

  • K. F. Roth

    (Imperial College of Science and Technology, Department of Mathematics)

Abstract

Let ℒ denote the set of all integers. Although ℒ is not itself a sequence, we shall sometimes use the phrase ‘subsequence of ℒ’ to describe a monotone strictly increasing sequence of integers. Let ℒ0 denote the sequence of all non-negative integers and ℒ1 the sequence of all natural numbers. Throughout the first five sections of this chapter the letters A, ℬ, C,... stand for subsequences of ℒ0; the letters a, b, c,... stand for elements of A, ℬ, C,... respectively.

Suggested Citation

  • H. Halberstam & K. F. Roth, 1983. "Addition of Sequences: Study of Density Relationships," Springer Books, in: H. Halberstam & K. F. Roth (ed.), Sequences, chapter 0, pages 1-75, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8227-0_1
    DOI: 10.1007/978-1-4613-8227-0_1
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