Clearly this relation is symmetric, reflexive, and transitive, so it is an equivalence relation and it can be used to separate the real numbers into equivalence classes. All the rational numbers are equivalent, because each rational number is equivalent to zero.
The symmetry, self-inclusion, and transitivity of this connection enable us to categorize real numbers into distinct groups based on their equivalence. Furthermore, the fact that all rational numbers are linked to zero underscores their shared characteristic.