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Sumterms, Summands, Sumtuples, and Sums and the Meta-Arithmetic of Summation

Scientific annals of computer science, 2020-01, Vol.30 (2), p.167-203 [Peer Reviewed Journal]

Copyright Alexandru Ioan Cuza University of Iasi 2020 ;ISSN: 1843-8121 ;EISSN: 2248-2695 ;DOI: 10.7561/SACS.2020.2.167

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  • Title:
    Sumterms, Summands, Sumtuples, and Sums and the Meta-Arithmetic of Summation
  • Author: Bergstra, Jan
  • Subjects: Names ; Operators ; Paradoxes ; Roles ; Splitting ; splitting paradox ; sumterms ; sumtuples
  • Is Part Of: Scientific annals of computer science, 2020-01, Vol.30 (2), p.167-203
  • Description: Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number. Sumterm splitting operators are introduced and it is argued that without further precautions the presence of these operators gives rise to an instance of the so-called sum splitting paradox. A survey of solutions to the sum splitting paradox is given.
  • Publisher: Iasi: Alexandru Ioan Cuza University of Iasi
  • Language: English
  • Identifier: ISSN: 1843-8121
    EISSN: 2248-2695
    DOI: 10.7561/SACS.2020.2.167
  • Source: ProQuest Central
    DOAJ Directory of Open Access Journals
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