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Basic properties of rational numbers
 Journal of Formalized Mathematics
, 1990
"... Summary. A definition of rational numbers and some basic properties of them. Operations of addition, subtraction, multiplication are redefined for rational numbers. Functors numerator (num p) and denominator (den p) (p is rational) are defined and some properties of them are presented. Density of ra ..."
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Cited by 43 (1 self)
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Summary. A definition of rational numbers and some basic properties of them. Operations of addition, subtraction, multiplication are redefined for rational numbers. Functors numerator (num p) and denominator (den p) (p is rational) are defined and some properties of them are presented. Density
Understanding rational numbers
"... Abstract Rational numbers are important as a foundation for later mathematics learning and particularly for learning algebra. Most researcher agree that students find rational numbers difficult. This article question the traditional use of partitioning as the starting point for the teaching of frac ..."
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Abstract Rational numbers are important as a foundation for later mathematics learning and particularly for learning algebra. Most researcher agree that students find rational numbers difficult. This article question the traditional use of partitioning as the starting point for the teaching
Efficient Rational Number Reconstruction
 Journal of Symbolic Computation
, 1994
"... this paper we describe how a variant of the algorithm in Jebelean [6] can be so adapted. In Section 2 we review the problem of rational reconstruction and the solution proposed by Wang, while fixing some notation and terminology along the way. We also discuss certain errors that have appeared in the ..."
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Cited by 26 (0 self)
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in the literature. Section 3 describes a multiprecision Euclidean algorithm for computing gcds that will be the basis of our algorithm. In Section 4 we discuss our algorithm and various details that are essential for an efficient implementation. 2 Reconstructing Rational Numbers
Automatic Sets of Rational Numbers
, 2014
"... The notion of a kautomatic set of integers is wellstudied. We develop a new notion — the kautomatic set of rational numbers — and prove basic properties of these sets, including closure properties and decidability. 1 ..."
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The notion of a kautomatic set of integers is wellstudied. We develop a new notion — the kautomatic set of rational numbers — and prove basic properties of these sets, including closure properties and decidability. 1
Approximating Rational Numbers by Fractions
"... Abstract. In this paper we show a polynomialtime algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both results ..."
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Abstract. In this paper we show a polynomialtime algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both
The Image of Rational Numbers in Students
"... Abstract: The concept of rational number is taught at all educational levels from primary school to the university. Nevertheless, results of an exam on rational numbers administered to an experimental group of high school and university students revealed that both have difficulty comprehending these ..."
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Abstract: The concept of rational number is taught at all educational levels from primary school to the university. Nevertheless, results of an exam on rational numbers administered to an experimental group of high school and university students revealed that both have difficulty comprehending
On the Gcompactification of the rational numbers
, 2009
"... We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbers Q such that X is its unique Gcompactification. This allows us to answer Problem 995 in the ‘Open Problems in Topology II ’ book in the negative: ther ..."
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We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbers Q such that X is its unique Gcompactification. This allows us to answer Problem 995 in the ‘Open Problems in Topology II ’ book in the negative
Vector rational number reconstruction
 In ISSAC 2011—Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation
, 2011
"... ABSTRACT The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d) 1≤i≤n from their images (ai) 1≤i≤n mod M , subject to a condition such as 0 < d ≤ N and ni ≤ N for a given magnitude bound N . Applying elementwise rationa ..."
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ABSTRACT The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d) 1≤i≤n from their images (ai) 1≤i≤n mod M , subject to a condition such as 0 < d ≤ N and ni ≤ N for a given magnitude bound N . Applying elementwise
Categorification of the Nonegative Rational Numbers
"... Abstract. In this document we describe a categorification of the semiring of natural numbers. We then use this result to construct a categorification of the semiring of nonnegative rational numbers. Acknowledgements: The author would like to thank Alistair Savage for his assistance and support throu ..."
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Abstract. In this document we describe a categorification of the semiring of natural numbers. We then use this result to construct a categorification of the semiring of nonnegative rational numbers. Acknowledgements: The author would like to thank Alistair Savage for his assistance and support
The Rational Numbers as a . . .
"... We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total functions and 12 equations. A consequence of this specification is that 0 −1 = 0, an interesting equation consistent with the ring axioms and many properties of divisi ..."
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We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total functions and 12 equations. A consequence of this specification is that 0 −1 = 0, an interesting equation consistent with the ring axioms and many properties
Results 1  10
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