# integer

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## integer:

see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
; number theorynumber theory,
branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
.

## integer

[′int·ə·jər]
(mathematics)
Any positive or negative counting number or zero.

## integer

any rational number that can be expressed as the sum or difference of a finite number of units, being a member of the set …--3, --2, --1, 0, 1, 2, 3…

## integer

(mathematics)
(Or "whole number") One of the finite numbers in the infinite set

..., -3, -2, -1, 0, 1, 2, 3, ...

An inductive definition of an integer is a number that is either zero or an integer plus or minus one. An integer is a number with no fractional part. If written as a fixed-point number, the part after the decimal (or other base) point will be zero.

A natural number is a non-negative integer.

## integer

A whole number. In programming, sending the number 123.398 to an integer function would return 123. Integers can be signed (positive or negative) or unsigned (always positive). If signed, the leftmost bit is used as the sign bit, and the maximum value of each sign is thus cut in half. For example, an 8-bit unsigned integer stores the values 0 to 255, whereas an 8-bit signed integer can store -128 to +127. See integer arithmetic and floating point.
References in periodicals archive ?
Let Z be the ring of integers and Q be a quasigroup defined by the following table;
Let Z be the ring of integers. Let Q be the quasigroup defined by the following table:
* 1 2 3 1I 21 3I 1 3 3 3 3I 3I 3I 2 3 3 3 3I 3I 3I 3 1 3 3 1I 3I 3I 1I 3I 3I 3I 3I 3I 3I 21 3I 3I 3I 3I 3I 3I 3I 1I 3I 3I 1I 3I 3I Let R = Z be the ring of integers. Then Z<S [union] I> is a
Example 4.4: Let <Z [union] I> be the ring of integers and let N (S) = {1,2,3,4,1I, 2I, 3I, 4I} be a neutrosophic LA-semigroup with the following table.
Take [Z.sub.6] = [Z.sub.2 x 3] = {0, 1, 2, 3, 4, 5} the ring of integers modulo 6.
Let <Z [union] I> be a neutrosophic ring of integers. Let (F, A) and (K, B) be two soft neutrosophic rings over <Z [union] I>.
As a consequence, we prove that there exist no D(4k + 2)-quadruples, k [member of] Z, in the ring of integers in Q([cube root of d]) for .
If [a.sup.2] [not equivalent to] [b.sup.2] (mod 9), then the ring of integers in Q([cube root of d]) equals Z[1,[alpha],[beta]].Otherwise, the ring of integers in Q([cube root of d]) is given by Z[[alpha], [beta], [gamma]],where [gamma] = [1 + a[alpha] + b[beta]]/3.
Let w = x + y[alpha] + z[beta] [member of] Z[1, [alpha], [beta]] denote an element of the ring of integers in a pure cubic field Q([cube root of d]).
Let w = 4x + 2 + y[alpha] + z[beta], x, y, z [member of] Z, denote an element of the ring of integers Z[1, [beta], [beta]] in a pure cubic field Q([cube root of d]), where d is even.
Let w = x[alpha] + y[beta] + z[gamma] [member of] Z[[alpha], [beta], [gamma]] denote an element of the ring of integers in a pure cubic field Q([cube root of d]), with even d = a[b.sup.2], where ab is square-free and [a.sup.2] = [b.sup.2] (mod 9).
Let w = x[alpha] + y[beta] +(4z + 2)[gamma], x, y, z [member of] Z, denote an element of the ring of integers Z[[alpha], [beta], [gamma]] in a pure cubic field Q([cube root of d]), where d is even.

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