Topologically, the set of subnets described by CIDR represent a [[Cover (topology)|cover]] of the corresponding address space. The interval described by the notation <math>X/n</math> numerically corresponds to addresses of the form (for IPv4) <math>[x \cdot 2^{32-n}, x \cdot 2^{32-n} + 2^{32-n} - 1]</math> (for IPv4) and <math>[x \cdot 2^{128n}, x \cdot 2^{128n} + 2^{128-n} - 1]</math> (for IPv6), where <math>X = x \cdot 2^{32-n}</math> and <math>X = x \cdot 2^{128-n}</math> has the lower <math>n</math> bits set to 0. (For IPv6, substitute 128 for 32.) For a fixed <math>n</math>, the set of all <math>X/n</math> subnets constitute a [[Partition of a set|partition]], that is a cover of non-overlapping sets. Increasing <math>n</math> yields finer and finer subpartitions. Thus two subnets <math>X/n</math> and <math>Y/m</math> are either disjoint or one is a subnet of the other.
