 For any rational number \(q\), there is a Dedekind cut corresponding to it, where \(L\) consists of the numbers strictly less than \(q\), while \(R\) consists of \(q\) and all larger numbers. However, there are also other partitions, where \(R\) does not contain a smallest element. For instance, we can let \(L\) include all the rational numbers whose cube is less than 2, while \(R\) includes all the rational numbers whose cube is greater than 2. Since there is no rational number whose cube is exactly equal to 2, this pair of sets forms a partition, representing the real number we think of as the cube root of 2.