Natural Numbers
Extensions of the System N of Natural Numbers Assigned to Primary Teachers
... This paper has resulted from a discussion conducted about which content of mathematics course should be the most suitable for the students of the insti- tutions where primary teachers are educated and when such a course ...
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A Survey of the System N of Natural Numbers Assigned to Primary Teachers
... The natural numbers are the basis from which all other number systems are ...the natural numbers to be a direct product of the human ...the natural numbers to be constructions ...
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An introduction of F graphs, a graph theoretic representation of natural numbers
... Cactus type graphs, core, pattern recognition, semigroup, semigroup isomorphism, natural numbers, ancestor graph, parent graph, descendant graph, Fgraph, attaching a graph, basis graph, [r] ...
5
Translation invariance and finite additivity in a probability measure on the natural numbers
... Inspired by the “two envelopes exchange paradox,” a finitely additive probability mea- sure m on the natural numbers is introduced. The measure is uniform in the sense that m({i}) = m({j}) for all i,j ∈ N. ...
5
Some Inequalities Involving the Geometric Mean of Natural Numbers and the Ratio of Gamma Functions
... In this article, using Stirling’s formula, the series-expansion of digamma functions and other techniques, two inequalities involving the geo- metric mean of natural numbers and the rati[r] ...
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The Effect of Time on Difficulty of Learning (The Case of Problem Solving with Natural Numbers)
... of natural numbers, writing exercises and problem posing for different ...of natural numbers and average math achievement ...with natural numbers", which is included in the ...
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Natural Numbers Applied to Physical Constants: Spacetime Discreteness
... We assume a spacetime discrete. Physical variables are considered as result of the sum of discrete contributions. Such discrete contributions can be calculated with the sum of natural numbers only. ...
8
On the Etale Fundamental Group of Schemes over the Natural Numbers
... the natural numbers. Indeed, the natural numbers are the foundation for all other systems of ...the natural numbers; the integers are derived from the natural ...
124
Teaching the Addition of Two Natural Numbers Within 5: A Study Based on “Mathematization”
... Figure 1 shows that the textbook "Mathematics 1” for primary schools of Vietnam builds the concept of natural numbers from 1 to 5 based on the cardinal numbers. Therefore, to present the addition ...
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SUCCESSIVE OCCURRENCE OF DIGIT 0 IN ALL BASE b NATURAL NUMBERS LESS THAN bn
... within natural numbers in the range, the count of its single and multiple occurrences and the first and last numbers for its appearances, formulae are derived for each of ...
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An Axiomatic Development of Multi-Natural Numbers
... We claim that this type of counting using multi- natural number preserves the essence of counting of the elements of a multiset and is favored by the addition of two multi-natural numbers. It’s worth ...
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Beyond sum free sets in the natural numbers
... Natural questions which now arise are: let N ∈ N ; then for a given s ∈ [1, N ], what are the minimum and maximum possible values of r(S) as S runs through all size-s subsets of [1, N]? (Consideration of ...
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Introduction to Mathematical Analysis I - Second Edition
... all natural numbers is a subset of R (and of any ordered field, in fact) by identifying the 1 in N with the 1 in axiom (2c) above, the number 2 with 1 + 1, 3 with 1 + 1 + 1, ...these numbers are ...
166
MoL 2018 14: Computation with Infinite Programs
... of natural numbers correspond to sets of strings in our framework, and similarly, infinite subsets of the natural numbers correspond to proper classes of ...of natural numbers is ...
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Problems in Strong Uniform Distribution
... We further specialize this theorem as follows. Let S = n≥1 N , i.e., the direct product of the natural numbers with themselves countably many times. The set S may also be described as the space of sequences ...
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Bio-Universe Model
... In the Bio-Universe Model, a multidimensional vacuum with n dimensions (n is the cardinal number of natural numbers) is the primordial structure of the universe that governs[r] ...
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A NEW SET THEORY FOR ANALYSIS
... of natural powers of ...the natural numbers that correspond to spaces in the sequence with a digit ...set numbers a, b, we say a < b if max ( a 4 b ) ∈ b, where a 4 b = ( a ∪ b ) − ( a ∩ b ...
23
Practical programming with total functions
... over natural numbers is that the use of arithmetic operations and pattern- matching on the induction variable does not force its type to be a natural number type: the compiler can typically ...
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MoL 2010 05: Non Standard Models of Arithmetic: a Philosophical and Historical perspective
... (6) I have shown in my reply, however, that these facts are still far from being adequate for completely characterising the nature of the number se- quence N . All these facts would hold also for every system S that, ...
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Error and Predicativity
... the natural numbers, and then use finite rules to extend this, by a process of successive ...of natural numbers according to the rule, then use this to build a new one, and so ...
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