What is Integer: Definition and 620 Discussions

An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers, and their additive inverses (the negative integers, i.e., −1, −2, −3, ...). The set of integers is often denoted by the boldface (Z) or blackboard bold



(

Z

)


{\displaystyle (\mathbb {Z} )}
letter "Z"—standing originally for the German word Zahlen ("numbers").ℤ is a subset of the set of all rational numbers ℚ, which in turn is a subset of the real numbers ℝ. Like the natural numbers, ℤ is countably infinite.
The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.

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  1. a1call

    Make Pari-gp Return Integer Instead of Modulo

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  2. kaliprasad

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  3. Albert1

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  4. avikarto

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  5. anemone

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  6. kaliprasad

    MHB Integer Solutions - Solve $a^2+b^2+c^2 + a + b+ c = 1$

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  7. rumborak

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  8. D

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  9. RJLiberator

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  11. B

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  12. anemone

    MHB What is the Greatest Integer When Evaluating a Complex Fraction?

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  13. anemone

    MHB Determine positive integer solutions

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  14. anemone

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  15. G

    C: Squaring string represented as positive integer

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  16. M

    MHB How can we prove that k is an integer?

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  17. anemone

    MHB Solve for positive integer solutions

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  18. W

    Number of non negative integer solutions to this inequality

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  19. P

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  20. SnakeDoc

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  21. anemone

    MHB Find the positive integer solutions

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  22. anemone

    MHB Solve for integer solutions

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  23. Md. Abde Mannaf

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  24. anemone

    MHB Solve for positive integer solutions

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  25. R

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  26. M

    MHB Prove Nonzero Integer Lemma in $F[t, t^{-1}]$

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  27. L

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  28. Y

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  29. Y

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  30. Y

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  31. T

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  32. C

    MHB Proving the integer that p is even and its square is even as well

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  33. Albert1

    MHB Integer S most close to A and less than A

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  34. avikarto

    Fortran [Fortran] Integer overflow for a real number?

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  35. Albert1

    MHB Find an integer most close to A

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  36. Puma

    Integer solutions to ax^2 + bx - cy^2 - dy = 0

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  37. anemone

    MHB Prove Existence of $n$ for Integer $\sqrt{n^3+xn^2+yn+z}$

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  38. C

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  39. andyrk

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  40. L

    Fortran Using Integer Expressions in an If Statement: Help Needed!

    Hi, so I'm trying to use the following if statement: if (sum(i,j) <=1.0 ) then sidash=(si)*(Death) else if (1 <= sum(i,j) <= 2) then sidash=(si)*((sqrt(2.0)+1.0)*(2.0-sum(i,j))*(Death)+(sum(i,j)-1.0)*(Survive)) else if (sum(i,j)<=3 .and. sum(i,j)=>2) then...
  41. B

    MHB Integer Factorization: Help with Pollards P-1 & Quadratic Sieve

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  42. C

    MHB Help on Fuzzy Integer Programming

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  43. G

    Mass dimension of coupling constant -- always an integer?

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  44. anemone

    MHB Prove a given number is an odd integer

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  45. J

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  46. C

    MHB (2+sqrt(3))^50 close to being an integer

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  47. D

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  48. anemone

    MHB Solving for Positive Integer $x$ and $y$ in $\dfrac{2^x}{y!}$

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  49. anemone

    MHB Solving for $3x+y+2z$ Given Integer Constraints

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  50. C

    MHB How Can Binary Integer Programming Optimize Subject Distribution in Schools?

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