murtolukuryhmän

Murtolukuryhmän is a Finnish term that translates to "fraction group" or "rational number group". It refers to the set of all rational numbers, denoted mathematically as Q. Rational numbers are numbers that can be expressed as a fraction p/q, where p is an integer and q is a non-zero integer. This includes all integers (e.g., 5 can be written as 5/1), terminating decimals (e.g., 0.75 can be written as 3/4), and repeating decimals (e.g., 0.333... can be written as 1/3).

The murtolukuryhmän forms a fundamental structure in abstract algebra. It is an abelian group under the operation of addition. This means that addition of rational numbers is commutative (a + b = b + a) and associative (a + (b + c) = (a + b) + c), there exists an additive identity (0, which is 0/1), and every rational number has an additive inverse (e.g., the inverse of a/b is -a/b).

Furthermore, the murtolukuryhmän is also a field. This means that in addition to the properties of an additive group, it is also an abelian group under multiplication (excluding zero), and multiplication distributes over addition. The set of rational numbers is dense, meaning that between any two distinct rational numbers, there exists another rational number. This property distinguishes it from the set of integers.