Definition:Integer/Also known as
Integer: Also known as
The integers are also referred to as whole numbers, so as to distinguish them from fractions.
However, use of this term is discouraged because it is ambiguous: it can refer to the integers, the positive integers, or the negative integers, depending on the preference of the author.
Some sources refer to the integers as rational integers, to clearly distinguish them from the algebraic integers.
Some sources use the term directed numbers or signed numbers for integers, so as to distinguish them from the natural numbers which are, by definition defined without a sign.
However, these terms are also used in the context of real numbers or rational numbers, so it is recommended that they not be used if integers specifically are meant.
Variants on $\Z$ are often seen, for example $\mathbf Z$, $\ZZ$ and $\mathfrak Z$, or even just $Z$.
Some sources use $I$, while others use $\mathbf J$ or a variant.
Sources
This page may be the result of a refactoring operation. As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering. If you have access to any of these works, then you are invited to review this list, and make any necessary corrections. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{SourceReview}} from the code. |
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.1$. Number Systems
- 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
- 1964: J. Hunter: Number Theory ... (previous) ... (next): Chapter $\text {I}$: Number Systems and Algebraic Structures: $1$. Introduction
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.1$. Sets: Example $1$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (next): $\S 0.1$. Arithmetic: Theorem $1$
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Introduction: Special Symbols
- 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): Appendix: Elementary set and number theory
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 1$. Introduction
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: The Notation and Terminology of Set Theory: $\S 1$
- 1971: Wilfred Kaplan and Donald J. Lewis: Calculus and Linear Algebra ... (previous) ... (next): Introduction: Review of Algebra, Geometry, and Trigonometry: $\text{0-1}$: The Real Numbers
- 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): Notation for Some Important Sets
- 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.8$: Collections of Sets: Definition $8.4$
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 4$: Number systems $\text{I}$: The rational integers
- 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $1$: Numbers: Real Numbers: $2$
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): Notation and Terminology
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: $\S 1.2$: The set of real numbers
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 2$: Introductory remarks on sets: $\text{(b)}$
- 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.1$ Divisibility of integers
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: The Real Number System: $2$
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $2$: Integers and natural numbers: $\S 2.1$: The integers
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): Glossary
- 1988: Dominic Welsh: Codes and Cryptography ... (previous) ... (next): Notation
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Integer
- 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.) ... (next): Notation and terminology
- 1994: H.E. Rose: A Course in Number Theory (2nd ed.) ... (previous) ... (next): Preface to first edition: Prerequisites
- 1994: H.E. Rose: A Course in Number Theory (2nd ed.) ... (previous) ... (next): $1$ Divisibility: $1.1$ The Euclidean algorithm and unique factorization
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.14$: Exercise $19 \ \text{(b)}$
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): Appendix $\text{A}.1$: Sets
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Glossary
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text A$: Sets and Functions: $\text{A}$: Set Theory: Countable Sets
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.2$: Elements, my dear Watson
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $3$: Notations and Numbers: Negative numbers