Results 11  20
of
2,880,058
Computing with classical real numbers
 CoRR
"... There are two incompatible Coq libraries that have a theory of the real numbers; the Coq standard library gives an axiomatic treatment of classical real numbers, while the CoRN library from Nijmegen defines constructively valid real numbers. Unfortunately, this means results about one structure cann ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
There are two incompatible Coq libraries that have a theory of the real numbers; the Coq standard library gives an axiomatic treatment of classical real numbers, while the CoRN library from Nijmegen defines constructively valid real numbers. Unfortunately, this means results about one structure
Familiarity with Real Numbers
"... What makes the real numbers so special? Create a lesson plan Gain an understanding of what teaching is like Gain experience in the classroom ..."
Abstract
 Add to MetaCart
What makes the real numbers so special? Create a lesson plan Gain an understanding of what teaching is like Gain experience in the classroom
Properties of the intervals of real numbers
 Journal of Formalized Mathematics
, 1993
"... Summary. The paper contains definitions and basic properties of the intervals of real numbers. The article includes the text being a continuation of the paper [4]. Some theorems concerning basic properties of intervals are proved. ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Summary. The paper contains definitions and basic properties of the intervals of real numbers. The article includes the text being a continuation of the paper [4]. Some theorems concerning basic properties of intervals are proved.
Basic Properties of Real Numbers
, 1989
"... this paper. A real number is an element of R. In the sequel x, y, z, t denote real numbers. One can prove the following two propositions: (9) 1 If z 6= 0 and x \Delta z = y \Delta z; then x = y: (10) If x + z = y + z; then x = y: Let x be a real number. The functor \Gammax yielding a real numbe ..."
Abstract
 Add to MetaCart
this paper. A real number is an element of R. In the sequel x, y, z, t denote real numbers. One can prove the following two propositions: (9) 1 If z 6= 0 and x \Delta z = y \Delta z; then x = y: (10) If x + z = y + z; then x = y: Let x be a real number. The functor \Gammax yielding a real
Formal and real authority in organizations
 The Journal of Political Economy
, 1997
"... This paper develops a theory of the allocation of formal authority (the right to decide) and real authority (the effective control over decisions) within organizations, and it illustrates how a formally integrated structure can accommodate various degrees of "real" integration. Real author ..."
Abstract

Cited by 845 (22 self)
 Add to MetaCart
of formal authority within organizations, the paper examines a number of factors that increase the subordinates ' real authority in a formally integrated structure: overload, lenient rules, urgency of decision, reputation, performance measurement, and multiplicity of superiors. Finally, the amount
Constructing the real numbers in HOL
, 1992
"... This paper describes a construction of the real numbers in the HOL theoremprover by strictly definitional means using a version of Dedekind's method. It also outlines the theory of mathematical analysis that has been built on top of it and discusses current and potential applications in verifi ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
This paper describes a construction of the real numbers in the HOL theoremprover by strictly definitional means using a version of Dedekind's method. It also outlines the theory of mathematical analysis that has been built on top of it and discusses current and potential applications
The Eudoxus Real Numbers
, 2004
"... Abstract. This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the wellknown construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek theory of proportion, d ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Abstract. This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the wellknown construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek theory of proportion
Computations with Effective Real Numbers
, 2004
"... A real number x is said to be effective if there wxists an algorithm which... In this paper, we review several techniques for computations with such numbers, and we will present some new ones ..."
Abstract
 Add to MetaCart
A real number x is said to be effective if there wxists an algorithm which... In this paper, we review several techniques for computations with such numbers, and we will present some new ones
Monotonically Computable Real Numbers
, 2001
"... A real number x is called kmonotonically computable (kmc), for constant k> 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is kmonotonic in the sense that k · x−xn  ≥ x−xm  for any m> n and x is monotonically computable (m ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
A real number x is called kmonotonically computable (kmc), for constant k> 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is kmonotonic in the sense that k · x−xn  ≥ x−xm  for any m> n and x is monotonically computable
Periods and elementary real numbers
, 805
"... The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced fr ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced
Results 11  20
of
2,880,058