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Showing 1 to 20 of 37 for “"Natural numbers"”.
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An Analysis of Models Used in Australia, Canada, Europe, and the United States to Provide An Understanding of Addition and Multiplication Over the Natural Numbers
Made available in DSpace on 2014-12-08T21:25:24Z (GMT). No. of bitstreams: 1 6915330.pdf: 22683088 bytes, checksum: 50633e821efea420dd09685fdc8ccb41 (MD5) Previous issue date: 1969
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Partition Theorems and Computability Theory
… sets for every computable 2-coloring of pairs of natural numbers, in an attempt to further understand the effective content of Ramsey's Theorem for exponent 2. We establish some new results about these degrees, and obtain as a corollary the nonexistence of a ""universal"" computable 2-coloring of …
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The Infinite Ladder in Mathematics: Transfinite Induction
… induction is mathematical induction beyond the natural numbers. These numbers are called ordinals, denoted by Greek letters. This thesis will introduce fundamental concepts of set theory, starting from the formal definition of natural numbers. We aim to provide a clear development of set theory …
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A utilização de jogos no ensino da matemática como instrumentos de aprendizagem no 5º ano do ensino fundamental.
… is positive, the construction operations with natural numbers. Participated in this study two groups of fifth grade of elementary school, a total of 28 children in the School Hall João Silvano. It was applied in the subjects in order to assess knowledge and conceptions about the use of games in …
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Arborescent numbers : higher arithmetic operations and division trees
The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary …
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Universal domains for sequential computation
… define all partial recursive functions over the natural numbers. However, most real programming languages support some form of higher-order data such as potentially infinite streams, lazy trees, and functions. Since these objects do not have finite canonical representations, computations over …
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O ensino de divisão com números naturais pela metodologia da resolução de problemas: aspectos teóricos.
… and reflections on teaching division with Natural Numbers in year 6 of primary education by the Solving Problems methodology with the intention to investigate and identify the guidelines and proposed activities for this content. The type of research chosen for the development of this study …
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Discrete Small Sample Asymptotics
Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Poisson approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and …
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Some Extremal Problems in Additive Number Theory
… squares, defined as the smallest sum of distinct natural numbers whose squares have sum n. Using a modified greedy algorithm, we give a precise asymptotic estimate for t(n) which shows, in particular, that t(n) is very closely approximated by n .
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The Asymptotic Behavior of Birkhoff- and Lacunary Sums
… functions and exponentially growing sequences of natural numbers. The corresponding summands often exhibit behavior typical of independent and identically distributed random variables. The methods used are of an analytical and probabilistic nature. The Birkhoff sums considered in this work are …
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Ramsey Algebras and Ramsey Spaces
… theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. Galvin and Glazer gave a brilliant simple proof of Hindman's theorem using idempotent ultrafilters. We study Ramsey algebras, which are structures that satisfy an analogue of Hindman's theorem. …
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Effective Versions of Ramsey's Theorem
… (the set of all unordered k-tuples of natural numbers) into finitely many classes, then there exists an infinite set A which is homogeneous for P; i.e., there exists $j, 1 \le j \le n,$ such that all k-tuples from A are in $C\sb{j}.$ Let H(P) denote the set of all infinite homogeneous …
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Connecting Number Theory with High School Mathematics
<p>Number theory is the study of natural numbers and one of the oldest branches of mathematics. Elementary number theory concepts are integrated into K-12 learning experience. This paper will identify ideas and methods in elementary number theory that could be connected to K-12 education and taught …
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A discussion of homogenous quadratic equations
… how to compute all Pythagorean triples and which numbers can be represented by the sum of two and four squares will be presented. Some concepts that follow from these theorems will also be presented. These include how to compute all Pythagorean Quadruples, which number can be represented by the …
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On the solutions of certain congruences
… lead to Wieferich primes and Wieferich numbers. In another direction this thesis explores the extensions of these concepts to other number fields such as quadratic fields of class number one. We also study the solutions of the congruence g^m - g^n ≡ 0 (mod f^m - f^n); where m and n are …
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I-magic labelings of cubic trees and n-caterpillars
… bijection from the set of edges E to the set of natural numbers less than or equal to q. A graph is said to be I-magic if there exists an edge labeling such that the sum of all edge labels incident to each internal vertex has the same value, and this value is called the magic index t, while the …
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The dichotomy in the determinacy of certain two-person infinite games with moves from {0,1}
… length. We consider games with moves from the natural numbers and games with moves from {0,1}. We show that the determinacy of open games with length o·n and with moves from {0,1} is true regardless of the existence of large cardinals for n ≥ 2. We show that this is not true, however, for …
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Binární znaménkové reprezentace celých čísel v kryptoanalýze hashovacích funkcí
… for the number of optimal D-representations of natural numbers with D = {0, 1, 3}. Keywords: hash function, MD5, binary signed digit representation (BSDR), non- adjacent form (NAF) 1
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Making Sense of Negative Numbers
Numbers are abstract objects that we conceptualize and make sense of through metaphors. When negative numbers appear in school mathematics, some properties of number sense related to natural numbers become contradictory. The metaphors seem to break down, making a transition from intuitive to formal …
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A study of the representational use of aggregates in the pedagogic elaboration of addition and subtraction in the Department of Basic Education Grades 1 to 3 Numeracy workbooks, prescribed for use in state funded South African schools
… aggregates in the teaching and learning of natural number addition and subtraction across the Foundation Phase of schooling. The central concern is the computational processes that use discrete aggregates, and operations over such aggregates. The six 2021 Department of Basic Education …
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