Every non-unit element of N, Z, Z[i], Z[ω], and Z[√2] is shown to be the sum-product of some non-trivial minimal multiset, with the lunar-arithmetic section containing a false lemma and false example.
Dismal Arithmetic
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abstract
Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take the smallest. This paper studies basic number theory in this world, including analogues of the primes, number of divisors, sum of divisors, and the partition function.
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math.RA 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Bioperational Multisets in Various Semi-rings
Every non-unit element of N, Z, Z[i], Z[ω], and Z[√2] is shown to be the sum-product of some non-trivial minimal multiset, with the lunar-arithmetic section containing a false lemma and false example.