In mathematics, the ε-covering number of a metric space (X, d), for some ε > 0, is the minimum number of balls of radius that are needed to cover X.
A related concept is the ε-packing number which is defined as the maximum number of disjoint balls of radius ε that fit into X.
Famous quotes containing the words covering and/or number:
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the childs life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)
“At thirty years a woman asks her lover to give her back the esteem she has forfeited for his sake; she lives only for him, her thoughts are full of his future, he must have a great career, she bids him make it glorious; she can obey, entreat, command, humble herself, or rise in pride; times without number she brings comfort when a young girl can only make moan.”
—Honoré De Balzac (17991850)