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rational numbers

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English

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Noun

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rational numbers

  1. plural of rational number

Noun

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rational numbers

  1. (mathematics) The set of numbers that can be expressed as a ratio of integers, often denoted with the bold letter Q, or the blackboard bold letter .
    • 2002, Michael Rosen, Number Theory in Function Fields, page vii:
      Elementary number theory is concerned with the arithmetic properties of the ring of integers, ℤ, and its field of fractions, the rational numbers, ℚ.
    • 2004, Ronald S. Irving, Integers, Polynomials, and Rings: A Course in Algebra, page 127:
      However, if our ring of interest is the rational numbers ℚ, then we see that [] .
    • 2012, Thomas E. Kieren, “3: Rational and Fractional Numbers: From Quotient Fields to Recursive Understanding”, in Thomas P. Carpenter, Elizabeth Fennema, Thomas A. Romberg, editors, Rational Numbers: An Integration of Research, page 53:
      In the analysis that follows, properties of an ordered quotient field (Birkhoff & MacLane, 1953) are considered, because this chapter is focusing on the rational numbers, a prime example of such a field.
    • For more quotations using this term, see Citations:rational numbers.

Usage notes

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In formal mathematical terms, the elements of the set can be expressed as fractions m/n, where m and n are integers and n is not zero. In set-builder notation, it can be denoted {m/n | m , n , n 0}.

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