rational number
The rational numbers are the fraction field of the ring of integers. In more elementary terms, a rational number is a quotient of two integers and , where is nonzero. Two fractions and are equivalent if the product of the cross terms is equal:
Addition and multiplication of fractions are given by the formulae
The field of rational numbers is an ordered field, under the ordering relation defined as follows: if
-
1.
the inequality holds in the integers, and has the same sign as , or
-
2.
the inequality holds in the integers, and has the opposite sign as .
Under this ordering relation, the rational numbers form a topological space under the order topology. The set of rational numbers is dense when considered as a subset of the real numbers.
Title | rational number |
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Canonical name | RationalNumber |
Date of creation | 2013-03-22 11:50:30 |
Last modified on | 2013-03-22 11:50:30 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 15 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13B30 |
Classification | msc 11A99 |
Classification | msc 03E99 |
Synonym | |
Related topic | Fraction |
Related topic | ProofThatTheRationalsAreCountable |
Defines | rational |