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...ence <math>\underline {within}</math> '''M''' of this set with the set of integers. ...

...lois field of order ''q'' = ''p^h''. where ''p, h'' are positive integers and ''p'' is a prime (the characteristic of the field), has recently been p ...

...the side be to the diagonal in a commensurable ratio, namely, that of two integers, ''a'' and ''b''. Suppose this ratio reduced to its lowest terms so that '' ...tions were called numbers. They used the word in the same sense as we use "integers." Hence numbers were conceived as ''discontinuous'', while magnitudes were ...

* The integers, the rationals, and the irrationals, taken together, make up the continuum ...

...thing else than the successive creation of the infinite series of positive integers in which each individual is defined by the one immediately preceding; the s ...ese numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of th ...

* The solution in integers, or in rational numbers, of indeterminate equations belongs to diophantine ...hereas the mathematicians of the classical period spoke only of a ratio of integers, not of parts of a whole and the ratios were used only in proportions.''' H ...

...the side be to the diagonal in a commensurable ratio, namely, that of two integers, ''a'' and ''b''. Suppose this ratio reduced to its lowest terms so that '' ...p''−1</sup>&nbsp;−&nbsp;1 whenever ''p'' is prime and ''a'' is [[w:Coprime integers|coprime]] to ''p'', now known as [[w:Fermat's little theorem|Fermat's littl ...

[[Category:Integers]] ...

=== ''[[wikipedia:God Created the Integers|God Created the Integers]]'' (2007) === <small>Full title: ''God Created the Integers: The Mathematical Breakthroughs That Changed History'' (2007).</small> ...

...more in the domain of modern algebra. The application of this work to the 'integers' of linear {{w|associative algebra}}s affords the ultimate extension up to ...theory of forms, in which the coefficients of the forms are either natural integers reduced [[w:Modular arithmetic|modulo]] ''p'', ''p'' [[w:Prime number|prime ...

...for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number ...

...the notion of absolute integers, it has gradually enlarged its domain. To integers have been added fractions, to rational quantities the irrational, to positi ...

...proof-sheets of Hardy on Ramanujan: 'As someone said, each of the positive integers was one of his personal friends.' My reaction was, 'I wonder who said that; ...

...he Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in th ...

...e, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly. <!--Ch.IV, p.82--> ...

...9, 16, 25, 36, 49, are given as the squares of the first seven [[w:Integer|integers]] respectively. We have next 1.4=8² 1.21=9² 1.40=10<s ...oked is the fact that '''in the''' [Babylonian] '''sexagesimal notation of integers the [[w:Positional notation|"principle of position"]] was employed.''' Thus ...

...nt sizes (called [[w:Cardinality|cardinalities]]). For example, the set of integers is [[w:Countable set|countably infinite]], while the set of real numbers is ....A class whose elements can be put in a one-to-one correspondence with the integers 1, 2, 3, ... is said to be [[w:Countable set|denumerable]]. All the points ...

[[Category:Integers]] ...

...of continuous magnitude, arithmetic was concerned with the discrete set of integers; and the two fields were irreconcilable.<!--p.7--> ...

...ant) hath a very full Treatise of Arithmetick in all the parts of it; in ''Integers, Fractions, Surds, Binomials''; ''Extraction of Roots, Quadratick, Cubick, ...