Real sets

George Janelidze*, Ross Street

*Corresponding author for this work

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    After reviewing a universal characterization of the extended positive real numbers published by Denis Higgs in 1978, we define a category which provides an answer to the questions:

    ·what is a set with half an element?

    ·what is a set with π elements?

    The category of these extended positive real sets is equipped with a countable tensor product. We develop somewhat the theory of categories with countable tensors; we call the commutative such categories series monoidal and conclude by only briefly mentioning the non-commutative possibility called ω-monoidal. We include some remarks on sets having cardinalities in [-∞,∞].

    Original languageEnglish
    Pages (from-to)23-49
    Number of pages27
    JournalTbilisi mathematical journal
    Issue number3
    Publication statusPublished - 2017

    Bibliographical note

    Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


    • Commutative monoid
    • biproduct
    • direct sum
    • abstract addition
    • magnitude module
    • series monoidal category


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