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...
متن کاملDivision by zero in non-involutive meadows
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 ...
متن کاملDivision by Zero in Common Meadows
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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.................................................................................... x 1 LITERATURE REVIEW......................................................................................... 1 1.1 Background in WDM Communication Networks................................. 1 1.2 Wavelength Demultiplexing In WDM Networks..................................... 1 1.3 Implementation of Wavelength D...
متن کاملAbout Division by 1
The Euclidean division of two formal series in one variable produces a sequence of series that we obtain explicitly, remarking that the case where one of the two initial series is 1 is sufficiently generic. As an application, we define a Wronskian of symmetric functions. The Euclidean division of two polynomials P (z), Q(z), in one variable z, of consecutive degrees, produces a sequence of line...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2016
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-016-0508-5