English

Noun

rational numbers

1. plural of rational number

Noun

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 ℚ.
   • 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, 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 examples of usage of this term, see Citations:rational numbers.

Usage notes

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 ∈ ℤ, n ∈ ℤ, n ≠ 0}.

Translations

References

• “rational number” in The American Heritage Dictionary of the English Language, Fourth Edition, Houghton Mifflin Company, 2000.
• “rational number” in Dictionary.com Unabridged, v1.0.1, Lexico Publishing Group, 2006.
• "rational number" in WordNet 2.0, Princeton University, 2003.