mathbbQ

The symbol mathbb{Q} represents the set of rational numbers. A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. The numerator, p, can be any integer (positive, negative, or zero), and the denominator, q, must be a non-zero integer.

The set of rational numbers includes all integers, as any integer n can be written as the fraction n/1. It also includes terminating decimals, such as 0.5 which is 1/2, and repeating decimals, such as 0.333... which is 1/3. Numbers that cannot be expressed as a simple fraction of two integers, like pi or the square root of 2, are called irrational numbers.

The set mathbb{Q} forms a field under the usual operations of addition and multiplication. This means that for any two rational numbers a and b, their sum (a+b), difference (a-b), product (a*b), and quotient (a/b, provided b is not zero) are also rational numbers. The rational numbers are dense on the number line, meaning that between any two distinct rational numbers, there exists another rational number.