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Sumterms are introduced as syntactic entities, and sumtuples are introducedas semantic entities. Equipped with these concepts a new description isobtained of the notion of a sum as (the name for) a role which can be played bya number. Sumterm splitting operators are introduced and it is argued thatwithout further precautions the presence of these operators gives rise toinstance of the so-called sum splitting paradox. A survey of solutions to thesum splitting paradox is given.

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