Recent Issues |
Abstract |
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We present three classes of abstract prearithmetics, , , and . The first is weakly projective with respect to the nonnegative real Diophantine arithmetic , the second is weakly projective with respect to the real Diophantine arithmetic , while the third is exactly projective with respect to the extended real Diophantine arithmetic . In addition, we have that every and every is a complete totally ordered semiring, while every is not. We show that the projection of any series of elements of converges in , for any , and that the projection of any nonindeterminate series of elements of converges in , for any , and in , for all . We also prove that working in and in , for any , and in , for all , allows us to overcome a version of the paradox of the heap. |
Keywords
non-Diophantine arithmetics, convergence of series, paradox of the heap
Mathematical Subject Classification
Primary: 03H15
Secondary: 03C62
Milestones
Received: 6 January 2021
Revised: 27 October 2021
Accepted: 11 March 2022
Published: 3 March 2023
Communicated by Kenneth S. Berenhaut
Authors
| Department of Statistical
Science Duke University Durham, NC United States |
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| Andrea Aveni | |
| Department of Statistical
Science Duke University Durham, NC United States |
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| Sayan Mukherjee | |
| Department of Statistical
Science Duke University Durham, NC United States |
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