In other words, <math>C_H^d(S)</math> is the [[infimum]] of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of [[ball (mathematics)|ball]]s <math>\{B(x_i,r_i):i\in I\}</math> covering ''S'' with ''r<sub>i</sub>'' > 0 for each ''i'' ∈ ''I'' that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that [[infimum|inf Ø = ∞]].) | In other words, <math>C_H^d(S)</math> is the [[infimum]] of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of [[ball (mathematics)|ball]]s <math>\{B(x_i,r_i):i\in I\}</math> covering ''S'' with ''r<sub>i</sub>'' > 0 for each ''i'' ∈ ''I'' that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that [[infimum|inf Ø = ∞]].) |