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

Jan A. Bergstra

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arXiv · 2009.08851

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

Jan A. Bergstra

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Abstract

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 instance of the so-called sum splitting paradox. A survey of solutions to the sum splitting paradox is given.

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Jan A. Bergstra. 2020-09-18. Sumterms, Summands, Sumtuples, and Sums and the Meta-arithmetic of Summation. https://arxiv.org/abs/2009.08851

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