Properties
- If S is a subset of n-dimensional Euclidean space Rn with its usual metric, then the packing dimension of S is equal to the upper modified box dimension of S:
- This result is interesting because it shows how a dimension derived from a measure (packing dimension) agrees with one derived without using a measure (the modified box dimension).
Note, however, that the packing dimension is not equal to the box dimension. For example, the set of rationals Q has box dimension one and packing dimension zero.
Read more about this topic: Packing Dimension
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)