Order of operations in elementary arithmetic

1962 ◽  
Vol 9 (5) ◽  
pp. 263-267
Author(s):  
Marvin L. Bender
Keyword(s):  
Natural Numbers ◽  
Whole Numbers ◽  
Restricted Sense

We will assume acquaintance with the set of natural numbers N = {1, 2, 3, …} and the set of whole numbers W = {0, 1, 2, 3, …}. The fundamental operations of addition and multiplication, and the related operations of subtraction and division will also be assumed as well known to the reader. It is to be understood that subtraction and division are operations only in a restricted sense, since it is not always possible to subtract or divide in the set of whole numbers. A recognition of a few of the properties of these operations, at least in form if not in name, will be assumed: in particular, the commutative and associative properties of addition and multiplication, and the fact that they do not hold for subtraction and division. Finally, an understanding of the meaning of the relations indicated by =(equal) and ≠ (not equal) will be assumed.

scholarly journals The Properties of the Arithmetic Function as the Consecutive Sum of Digits in Natural Numbers

2021 ◽  
Author(s):  
Ramazanali Maleki Chorei
Keyword(s):  
Natural Number ◽  
Diophantine Equations ◽  
Arithmetic Function ◽  
Arithmetic Functions ◽  
Natural Numbers ◽  
Whole Numbers ◽  
Sum Of Digits ◽  
Dimensional Equation

In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.

scholarly journals DIAGNOSTICS OF MATHEMATICAL PROOF OF THE BEAL CONJECTURE IN MEDICAL PSYCHOLOGY (REMAKE OF PREVIOUS AUTHOR’S ARTICLES CONCERNING FERMAT’S LAST THEOREM)

2021 ◽  
Vol 1 (5(69)) ◽  
pp. 28-33
Author(s):  
Y. Ivliev
Keyword(s):  
Mathematical Proof ◽  
Mathematical Structure ◽  
Pythagorean Theorem ◽  
Medical Psychology ◽  
Natural Numbers ◽  
Whole Numbers ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem ◽  
The Given ◽  
Infinite Descent

In the given work diagnostics of mathematical proof of the Beal Conjecture (Generalized Fermat’s Last Theorem) obtained in the earlier author’s works was conducted and truthfulness of the suggested proof was established. Realizing the process of the Bill Conjecture solution, the mathematical structure defining hypothetical equality of the Fermat theorem was determined. Such a structure turned to be one of Pythagorean theorem with whole numbers. With help of Euclid’s geometrical theorem and Fermat’s method of infinite descent one can manage to set that Pythagorean equation in whole numbers representing Fermat’s Last Theorem cannot exist and then the Fermat theorem is true, that is Fermat’s equality in natural numbers does not exist. Thus mental scheme of “demonstratio mirabile”, which Pierre de Fermat mentioned on the margins of Diophantus’s “Arithmetic”, was reconstructed. 

Discovering properties of the natural numbers

1965 ◽  
Vol 12 (8) ◽  
pp. 627-632
Author(s):  
Harriet Griffin
Keyword(s):  
Elementary School ◽  
Natural Numbers ◽  
Whole Numbers ◽  
Mathematical Properties ◽  
Mathematical Rule ◽  
Insight Into

Have you ever known the joy of discovering a mathematical rule or relation? Surely you can recall the feeling of satisfaction that comes from finding a proof of a theorem, whether or not you formulated its statement. In this paper we propose to review some of the basic rules about t he natural numbers 1, 2, 3, etc., often called the whole numbers or arithmetic integers, to show that these numbers provide the superior student in the upper grades of the elementary school with many opportunities for discerning mathematical properties. Such considerations will not only sharpen the student's insight into like problems, but will also help him to develop a relish for such thoughtful activity. Investigations he can make independently, after some fundamental ideas have been explained, will also convince him of the need for distinguishing between the process of examining objects to draft a statement about a characteristic they possess and the task of constructing a proof to show whether or not the statement is correct.

scholarly journals The Methods of Solving Equations Ax+By=Cz with Co-Prime A, B, C, where x≥2,y≥2,x≥2 Are Natural Numbers, Equal the Two only in one of the Three Possible Cases - The Proof of Catalan's Conjecture

2013 ◽  
Vol 8 ◽  
pp. 17-25
Author(s):  
K. Raja Rama Gandhi ◽  
Reuven Tint ◽  
Michael Tint
Keyword(s):  
Infinite Number ◽  
Natural Numbers ◽  
Whole Numbers ◽  
Solving Equations ◽  
Solutions Of Equations

One of the principal problems of the Beal's conjecture, as we see that, is methods for finding a pairwise coprime solution which is defined below. First found methods and identities, allowing receiving infinite number solutions of equations as Ax+By=Cz for co-prime integers arranged in a pair (A,B,C)=1 are natural (whole) numbers, where a fixed permutation (x,y,z)corresponds to each of the permutations (2,3,4), (2,4,3), (4,3,2) Here we obtain also our method and identities of all not recurrent and not co-prime solutions of the above type, part of which has already been published, in contrast to the method of obtaining the recurrence not co-prime solutions of this type from [(1), W. Sierpiński, p. 21-25, 63]. As the solution of the main problem appeared additional problems that solved by obtained appropriate identities. Given as two equal proofs of Catalan's Conjecture.

New Publications

1974 ◽  
Vol 67 (2) ◽  
pp. 152-155
Keyword(s):  
Word Problems ◽  
Rational Numbers ◽  
Natural Numbers ◽  
Irrational Numbers ◽  
Whole Numbers

The text provides a refresh on these topics: natural numbers, whole numbers, integers, rational numbers, decimals, and irrational numbers. There are two final chapters on geometry and selected applications. A good many “word” problems are included, along with lots of drill exercises. Exposition is rather brief. The treatment of topics is elementary throughout.— Skeen.

scholarly journals Prime Numbers Calculation Formulas

2021 ◽  
pp. 1-6
Author(s):  
Ameha Tefera Tessema
Keyword(s):  
Computer Science ◽  
Prime Number ◽  
Modern Science ◽  
Prime Numbers ◽  
Jel Classification ◽  
Natural Numbers ◽  
Whole Numbers ◽  
Number Distribution

The application of prime numbers in modern science, especially in computer science, is very wide. Since prime numbers can only divisible by 1 and themselves, they are not factored any further like whole numbers. The problem to calculate all prime numbers using a formula posed for long periods. Though different formulas to calculate prime numbers were developed by Euler, Fermat, Mersenne and others, the formulas work for limited natural numbers and calculate limited prime numbers. JEL classification numbers: C02, C63, C69 Keywords: Prime numbers, Prime numbers formula, Prime number distribution, Prime number calculation.

The Argument from (Natural) Numbers

2018 ◽  
Author(s):  
Tyron Goldschmidt
Keyword(s):  
Natural Numbers ◽  
Existence Of God ◽  
Divine Attribute ◽  
Rule Out

This chapter considers Plantinga’s argument from numbers for the existence of God. Plantinga sees divine psychologism as having advantages over both human psychologism and Platonism. The chapter begins with Plantinga’s description of the argument, including the relation of numbers to any divine attribute. It then argues that human psychologism can be ruled out completely. However, what rules it out might rule out divine psychologism too. It also argues that the main problem with Platonism might also be a problem with divine psychologism. However, it will, at the least, be less of a problem. In any case, there are alternative, possibly viable views about the nature of numbers that have not been touched by Plantinga’s argument. In addition, the chapter touches on the argument from properties, and its relation to the argument from numbers.

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