Continued function expansions of real numbers
نویسندگان
چکیده
منابع مشابه
Expansions of Real Numbers
It was discovered some years ago that there exist non-integer real numbers q > 1 for which only one sequence (ci) of integers 0 ≤ ci < q satisfies the equality P ∞ i=1 ciq −i = 1. The set U of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation. For each fi...
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It was discovered some years ago that there exist non-integer real numbers q > 1 for which only one sequence (ci) of integers 0 ≤ ci < q satisfies the equality P∞ i=1 ciq −i = 1. The set U of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation. For each fix...
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The familiar continued fraction expansion of a real number has great importance in its approximation by rational numbers, and the predictable behavior of the continued fractions of certain classes of real numbers has added benefits. For example, the fact that the continued fraction expansion of a rational number terminates is essentially a reexpression of the Euclidean algorithm; also, the peri...
متن کاملOn the real quadratic fields with certain continued fraction expansions and fundamental units
The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element where $dequiv 2,3( mod 4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and $n_d$ and $m_d...
متن کاملLecture 18: The Constructive Real Numbers Continued
This lecture continues our discussion of the constructive reals and intuitionistic reals. We look at other options beyond the approach taken in the book Constructive Analysis by Bishop and Bridges which is a resource for this course available on the PRL project page (www.nuprl.org). Another resource is the calculator for the constructive reals provided in Nuprl as a public resource. It uses alg...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1960-0122753-7