rational numbers
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English
Noun
Noun
- (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”, 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
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
set of numbers that can be expressed as a ration of integers
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References
- “rational number”, in The American Heritage Dictionary of the English Language, 4th edition, Boston, Mass.: Houghton Mifflin, 2000, →ISBN.
- “rational number”, in Dictionary.com Unabridged, Dictionary.com, LLC, 1995–present.
- "rational number" in WordNet 2.0, Princeton University, 2003.