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Basic Properties of Real Numbers
 Journal of Formalized Mathematics
, 1989
"... this paper. A real number is an element of R ..."
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 116 (14 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification
PCF extended with real numbers
, 1996
"... We extend the programming language PCF with a type for (total and partial) real numbers. By a partial real number we mean an element of a cpo of intervals, whose subspace of maximal elements (singlepoint intervals) is homeomorphic to the Euclidean real line. We show that partial real numbers can be ..."
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Cited by 54 (15 self)
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We extend the programming language PCF with a type for (total and partial) real numbers. By a partial real number we mean an element of a cpo of intervals, whose subspace of maximal elements (singlepoint intervals) is homeomorphic to the Euclidean real line. We show that partial real numbers can
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 574 (50 self)
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We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given
Topological Properties of Subsets in Real Numbers
 JOURNAL OF FORMALIZED MATHEMATICS
, 2002
"... ..."
Real numbers and other completions
, 2007
"... A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete ..."
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Cited by 7 (0 self)
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A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete
BASES FOR INTERVALS OF REAL NUMBERS
"... In this paper we discuss the problem of representing uniquely each real number in the interval (0, c] , where c is any positive real number, as an infinite series of terms selected from a sequence (b) of real numbers. choose an integer k ^ 1 and require that any two terms of (b) whose suffices ..."
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In this paper we discuss the problem of representing uniquely each real number in the interval (0, c] , where c is any positive real number, as an infinite series of terms selected from a sequence (b) of real numbers. choose an integer k ^ 1 and require that any two terms of (b) whose suffices
The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 682 (76 self)
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.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R
Construction Of The Real Number System
"... Currently, there is no modules in the mathematics department of NUS that offer a rigorous treatment of the construction of the real number system. The real number system is simply taken for granted, with all its associated properties. Although this current approach of assuming the existence of the r ..."
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Currently, there is no modules in the mathematics department of NUS that offer a rigorous treatment of the construction of the real number system. The real number system is simply taken for granted, with all its associated properties. Although this current approach of assuming the existence
On statistically convergent sequences of real numbers
 Math. Slovaca
"... The notion of the statistical convergence of sequences of real numbers was introduced in papers [1] and [5]. In the present paper we shall show that the set of all bounded statistically convergent sequences of real numbers is a nowhere dense subset of the linear normed space m (with the supnorm) of ..."
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Cited by 63 (1 self)
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The notion of the statistical convergence of sequences of real numbers was introduced in papers [1] and [5]. In the present paper we shall show that the set of all bounded statistically convergent sequences of real numbers is a nowhere dense subset of the linear normed space m (with the sup
Results 1  10
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2,880,058