Definition of integer in English:



  • 1A number which is not a fraction; a whole number:

    [as modifier] ‘integer values’
    • ‘In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.’
    • ‘Marshall Hall showed talent for mathematics at a young age when he constructed a seven-place table of logarithms for the positive integers up to 1000.’
    • ‘Whole numbers or integers are often the subject of such pursuits.’
    • ‘I'm going to give you the whole picture: how to work with both integers and fractions in other bases.’
    • ‘Fibonacci proves that the root of the equation is neither an integer nor a fraction, nor the square root of a fraction.’
    • ‘Here are the whole numbers/natural numbers/positive integers up to 700, in binary columns.’
    • ‘What about those integers in the continued fraction forms of the powers?’
    • ‘The floor function rounds down by taking a non-integer value to the next integer below it.’
    • ‘A perfect number is a whole number, an integer greater than zero; and when you add up all of the factors less than that number, you get that number.’
    • ‘Clearly, most integers are not squares of whole numbers.’
    • ‘A second work is the Book of the Number which describes the decimal system for integers with place values from left to right.’
    • ‘When talking about modular arithmetic it is important to remember that we are only allowed to use integers, that is whole numbers.’
    • ‘In the continued fraction of the square root of an integer the same denominators recur periodically.’
    • ‘Possibly as a consequence of that, the Greek mathematicians thought of fractions in terms of ratios of integers, rather than numbers.’
    • ‘By contrast, which is sometimes overlooked, in the arithmetical Books 7-9 multiplication of integers themselves occurs as usual.’
    • ‘The row of numerators starts with the pair of integers 0,1.’
  • 2A thing complete in itself.


Early 16th century (as an adjective meaning ‘entire, whole’): from Latin, intact, whole, from in- (expressing negation) + the root of tangere to touch. Compare with entire, also with integral, integrate, and integrity.