# integer

## Definitions

• WordNet 3.6
• n integer any of the natural numbers (positive or negative) or zero "an integer is a number that is not a fraction"
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Webster's Revised Unabridged Dictionary
• n Integer A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
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Century Dictionary and Cyclopedia
• n integer An entire entity; particularly, in arithmetic, a whole number, in contradistinction to a fraction. Thus, in the number 54.7, 54 is an integer, and .7 a fraction (seven tenths of a unit).
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Chambers's Twentieth Century Dictionary
• n Integer in′te-jėr that which is left untouched or undiminished, a whole:
• n Integer a whole: the whole as made up of its parts
• n Integer in′te-jėr (arith.) a whole number, as opposed to a fraction
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## Etymology

Webster's Revised Unabridged Dictionary
L. integer, untouched, whole, entire. See Entire
Chambers's Twentieth Century Dictionary
L.,—in, not, root of tangĕre, to touch.

## Usage

### In literature:

But away from his home the sport is an integer.
"The Voice of the City" by O. Henry
But just before the catastrophe one man, integer vitae scelerisque purus, sees the truth.
"The Longest Journey" by E. M. Forster
An integer or two would be more useful to maintain the integrity of the House.
"Punchinello, Vol. 1, No. 6, May 7, 1870" by Various
No integer of the impressionable sex had ever yet won from her such a battle.
"The Clarion" by Samuel Hopkins Adams
Dealing with the problem generally, 12n+9 boys may walk out in triplets under the conditions on 9n+6 days, where n may be nought or any integer.
"Amusements in Mathematics" by Henry Ernest Dudeney
In the village separate home integers appear ideal; in the city they are possible only to the few.
"Religious Education in the Family" by Henry F. Cope
Now, since a, B, b, A, are integers, so also is P; and thence Q; and thence R, etc.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
Never, in all the thousands of years of shepherding, have they come to recognize man as an integer.
"The Free Range" by Francis William Sullivan
F., I find 777 to the nearest integer.
"Scientific American Supplement, No. 647, May 26, 1888" by Various
We are to form ourselves on the model of the integer rather than the fraction of humanity.
"The History of Dartmouth College" by Baxter Perry Smith
For these reasons among others our interest in Dickens's novels as integers has diminished and is diminishing.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 4" by Various
The general form of these is ax^n + bx^{n-1} + ... + kx + l = 0, where n is a positive integer, and a, b, ... k, l are given numbers.
"The New Gresham Encyclopedia" by Various
The simplest case which thus presents itself is that in which there are two variables while the coefficients are rational integers.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
Two integers are in the ratio 4 : 5.
"A Review of Algebra" by Romeyn Henry Rivenburg
INTEGER VITAE SCELERISQUE PURUS (L.), blameless in life and clear of crime.
"Chambers's Twentieth Century Dictionary (part 4 of 4: S-Z and supplements)" by Various
It will save more time in the work with integers than was spent in teaching it!
"The Psychology of Arithmetic" by Edward L. Thorndike
This integer is supposed known.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 6" by Various
If q is an integer and p = r/s we put 1 + t = u^s.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5" by Various
Voracity thus as an integer stands For his diurnal gorge on multiplicands.
"The Bee's Bayonet" by Edwin Alfred Watrous
I felt he was going again over 'fractions' and the 'integers.
"The Secret of Charlotte Brontë" by Frederika Macdonald
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### In poetry:

"And the great fight raged furious all the night
Till every integer was made a fraction;
Reader, wouldst know what history has to show
As net result of the above transaction?
"How To Not Settle It" by Oliver Wendell Holmes
Each fall the children must endure together
What every child also endures alone:
Learning the alphabet, the integers,
Three dozen bits and pieces of a stuff
So arbitrary, so peremptory,
That worlds invisible and visible
"September, The First Day Of School" by Howard Nemerov

### In news:

Aliquam A Vel Integer Vel Lorem Ipsum Pellentesque Et Nullam.
Students were assigned a project in which they were required to make a board game that involved addition, subtraction and/or comparison of integers with a partner.
Integer Research has launched a monthly diesel exhaust fluid (DEF) price reporting service called DEF Tracker.
Stefan Leue, Wei Wei, " Integer Linear Programming Based Property Checking for Asynchronous Reactive System," IEEE Transactions on Software Engineering, vol 99, no.
Entering the sequence 2, 3, 4, 6, 7, 8, 11, 12 in the search box, for example, yields five results—known sequences that contain this particular string of consecutive integers .
The below picture gives a map of the complexity -- that is, the necessary number of i 's -- for complex integers -100-100 i to 100+100 i.
The complexity of the complex integers .
}, with various definitions of ?, that will produce all positive integers .
Rose, H Hellerman, "Portable Character Processing in Fortran and Fixed Integer Environments," IEEE Transactions on Software Engineering, vol 2, no.
Each nonwoven connector may be folded n times wherein n is an integer of front 2 to 30.
The Prime Number theorem says that the probability P(x) that a large integer x is prime is about 1/log x.
Journal of Integer Sequences 2(Oct 17).
One of the greatest singers in the history of country music, Patsy Cline also helped blaze a trail for female singers to assert themselves as an integ.
However, ddPCR enables 1.2×-fold differences to be measured and can easily discriminate between integer gene copies .
The price of diesel exhaust fluid at the pump jumped in August while tote prices remained level, according to the latest DEF Tracker price update from Integer Research.
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### In science:

We call a pair of integers (i, j ) related if and only if there exists an integer h with 1 ≤ h ≤ g − 1 such that (i, j ) = (2h − 1, 2h).
Large characteristic subgroups of surface groups not containing any simple loops
Denote by Z the ring of integers and by N the set of nonnegative integers.
Simple Conformal Algebras Generated by Jordan Algebras
Any unitary irreducible representation of the group SU (2) is determined by nonnegative integer or half-integer j .
Smooth Loops, Generalized Coherent States and Geometric Phases
Moreover, we denote by Z the ring of integers and by N the additive semi-group of nonnegative integers.
Central Simple Poisson Algebras
This is reﬂectable in the same chamber if m is an integer or half-integer.
Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
Deﬁnition: Let p be the smallest positive integer in the value semigroup, and q be the smallest integer in the semigroup which is greater than p and is not a multiple of p.
Simple singularities of multigerms of curves
X~κ where ~κ = ~kL/(2π) is the dimensionless wavenumber; it is an integer or half-integer triplet with components κi ∈ [−M /2, M /2).
Multiscale Gaussian Random Fields for Cosmological Simulations
For integer β the singular term is corrected by a logarithmic factor; hence, the critical exponents are obtained by taking the smooth limit β → integer. Actually, the observable scaling like (λc − λ)−1 is hN p i1/p with not too small p. J.
Statistical ensemble of scale-free random graphs
For Euclid all integers are positive — and ordered, indeed well ordered, meaning no sequence of positive integers in which each member is less than its predecessor can be an inﬁnite sequence, but must terminate after ﬁnitely many terms.
Factorization of integers and arithmetic functions
For this special case, we observe ﬁrst that integers form a subring of each ﬁeld F considered before, and the ring of sequences of integers is a subring of each of the corresponding rings R.
Factorization of integers and arithmetic functions
Int(n(1 + v )/2) + 1, where Int(x) is the integer part of x, i.e., the largest integer less than or equal to x.
Statistics of the occupation time for a random walk in the presence of a moving boundary
We consider the case with qR = k + 1/n, where k is an integer and n is a positive integer.
Properties of String Theory on Kaluza-Klein Melvin Background
Deﬁnition 2.13 A partition of an integer n is a non-increasing list of positive integers with sum equal to n.
An algorithm to generate exactly once every tiling with lozenges of a domain
Deﬁnition 2.15 A plane partition of an integer n is a ﬁlling of a Ferrers diagram with integers (of sum n), such that the values along the rows and the columns is non-increasing.
An algorithm to generate exactly once every tiling with lozenges of a domain
We will take as canonical representatives of the nonzero cyclic groups the groups Zm , the integers mod m, where m is either 0 or an integer larger than 1.
\$K_0\$ of purely infinite simple regular rings
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