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96
Topological Properties of Subsets in Real Numbers
 JOURNAL OF FORMALIZED MATHEMATICS
, 2002
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An Overview of the MIZAR Project
 UNIVERSITY OF TECHNOLOGY, BASTAD
, 1992
"... The Mizar project is a longterm effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system ..."
Abstract

Cited by 94 (1 self)
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The Mizar project is a longterm effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system developed by Ja'skowski. The texts written in the language are called Mizar articles and are organized into a data base. The TarskiGrothendieck set theory forms the basis of doing mathematics in Mizar. The implemented processor of the language checks the articles for logical consistency and correctness of references to other articles.
Convergent Real Sequences. Upper and Lower Bound of Sets of Real Numbers
, 2000
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Metric spaces
 Formalized Mathematics
, 1990
"... Summary. Sequences in metric spaces are defined. The article contains definitions of bounded, convergent, Cauchy sequences. The subsequences are introduced too. Some theorems concerning sequences are proved. ..."
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Cited by 55 (3 self)
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Summary. Sequences in metric spaces are defined. The article contains definitions of bounded, convergent, Cauchy sequences. The subsequences are introduced too. Some theorems concerning sequences are proved.
Real Function Continuity
, 2002
"... this paper. For simplicity, we adopt the following convention: n denotes a natural number, X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 0 , x 1 , x 2 denote real numbers, s 1 denotes a sequence of real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R ..."
Abstract

Cited by 47 (8 self)
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this paper. For simplicity, we adopt the following convention: n denotes a natural number, X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 0 , x 1 , x 2 denote real numbers, s 1 denotes a sequence of real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R
A Theory of Boolean Valued Functions and Partitions, Formalized Mathematics
, 1998
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The limit of a real function at infinity
 Journal of Formalized Mathematics
, 1990
"... Summary. We introduced the halflines (open and closed), real sequences divergent to infinity (plus and minus) and the proper and improper limit of a real function at infinty. We prove basic properties of halflines, sequences divergent to infinity and the limit of function at infinity. ..."
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Cited by 33 (5 self)
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Summary. We introduced the halflines (open and closed), real sequences divergent to infinity (plus and minus) and the proper and improper limit of a real function at infinty. We prove basic properties of halflines, sequences divergent to infinity and the limit of function at infinity.
MooreSmith Convergence
, 2003
"... The paper introduces the concept of a net (a generalized sequence). The goal is to enable the continuation of the translation of [14]. ..."
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Cited by 32 (2 self)
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The paper introduces the concept of a net (a generalized sequence). The goal is to enable the continuation of the translation of [14].