Editing Classless Inter-Domain Routing (section)

==Numerical interpretation==
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>, where <math>X = x \cdot 2^{32-n}</math> has the lower <math>n</math> bits set to 0.  (For IPv6, substitute 128.)  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.