Mathematics Journal: Division of Zero by Itself - Division of Zero by Itself Has Unique Solution
نویسندگان
چکیده
منابع مشابه
Division by zero
For any sufficiently strong theory of arithmetic, the set of Diophantine equations provably unsolvable in the theory is algorithmically undecidable, as a consequence of the MRDP theorem. In contrast, we show decidability of Diophantine equations provably unsolvable in Robinson’s arithmetic Q. The argument hinges on an analysis of a particular class of equations, hitherto unexplored in Diophanti...
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Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study 'non-involutive meadows', i.e. variants of meadows ...
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Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with a that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero tha...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Journal
سال: 2018
ISSN: 2326-9790
DOI: 10.11648/j.pamj.20180703.11