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36
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 ..."
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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
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.
Trigonometric Functions and Existence of Circle Ratio
 Journal of Formalized Mathematics
, 1998
"... this article, we defined sinus and cosine as real part and imaginary part of exponential function on complex, and gave thier series expression either. Then we proved the differentiablity of sin, cos and exponential function of real. At last, we showed the existence of circle ratio, and some formulas ..."
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Cited by 13 (1 self)
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this article, we defined sinus and cosine as real part and imaginary part of exponential function on complex, and gave thier series expression either. Then we proved the differentiablity of sin, cos and exponential function of real. At last, we showed the existence of circle ratio, and some formulas of sin, cos. MML Identifier: SINCOS.
The limit of a real function at a point
 Journal of Formalized Mathematics
, 1990
"... Summary. We introduce the leftside and the rightside limit of a real function at a point. We prove a few properties of the operations on the proper and improper oneside limits and show that Cauchy and Heine characterizations of the oneside limit are equivalent. ..."
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Cited by 7 (1 self)
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Summary. We introduce the leftside and the rightside limit of a real function at a point. We prove a few properties of the operations on the proper and improper oneside limits and show that Cauchy and Heine characterizations of the oneside limit are equivalent.
Inverse Trigonometric Functions arctan and arccot
 FORMALIZED MATHEMATICS VOL. 16, NO. 2, PAGES 147–158, 2008
, 2008
"... This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several differentiation formulas of arctan and arccot. ..."
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Cited by 7 (3 self)
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This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several differentiation formulas of arctan and arccot.
Inverse Trigonometric Functions Arcsin and Arccos
, 2005
"... Notions of inverse sine and inverse cosine have been introduced. Their basic properties have been proved. ..."
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Cited by 6 (0 self)
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Notions of inverse sine and inverse cosine have been introduced. Their basic properties have been proved.
Definition of Integrability for Partial Functions from R to R and Integrability for Continuous Functions
"... Summary. In this article, we defined the Riemann definite integral of partial function from R to R. Then we have proved the integrability for the continuous function and differentiable function. Moreover, we have proved an elementary theorem of calculus. ..."
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Cited by 3 (0 self)
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Summary. In this article, we defined the Riemann definite integral of partial function from R to R. Then we have proved the integrability for the continuous function and differentiable function. Moreover, we have proved an elementary theorem of calculus.
Real Function Uniform Continuity
, 1990
"... this paper. For simplicity, we adopt the following convention: X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 1 , x 2 denote real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R ..."
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Cited by 3 (1 self)
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this paper. For simplicity, we adopt the following convention: X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 1 , x 2 denote real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R
SecondOrder Partial Differentiation of Real Binary Functions
"... Summary. In this article we define secondorder partial differentiation of real binary functions and discuss the relation of secondorder partial derivatives and partial derivatives defined in [17]. ..."
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Cited by 3 (0 self)
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Summary. In this article we define secondorder partial differentiation of real binary functions and discuss the relation of secondorder partial derivatives and partial derivatives defined in [17].