|Definition:|| element of a set of mathematical entities that includes all integers and other entities, each defined as the quotient of two integers, such that the division is defined for any two entities, except zero as a divisor|
Note 1 to entry: Any of the ordered pairs 2/1, 4/2, 6/3, ..., −2/(−1), −4/(−2), ... represents the rational number identified with the integer 2. Any of the ordered pairs 2/3, 4/6, 6/9, ... −2/(−3), −4/(−6), ... represents the rational number which is the quotient of the integer 2 by the integer 3, also denoted by "0,666 6...".
Note 2 to entry: The operations of addition, subtraction, multiplication and division, except the division by zero, are defined for any two rational numbers. Any rational number has a negative. Any non-zero rational number has an inverse.
Note 3 to entry: There is a total order on the set of rational numbers.
Note 4 to entry: In the decimal representation of a rational number other than an integer, the sequence of digits after the decimal sign is either finite or periodically repeated after some position.
Note 5 to entry: The set of rational numbers is denoted by ℚ (Q with vertical bars in the left and right arcs), or Q, or sometimes Q with a vertical bar in the left arc. This set without zero is denoted by an asterisk to the symbol, for example ℚ*.