Comparison To Classical Dimension
If Z is a subset of 2ω, its Hausdorff dimension is .
The packing dimension of Z is .
Thus the effective Hausdorff and packing dimensions of a set are simply the classical Hausdorff and packing dimensions of (respectively) when we restrict our attention to c.e. gales.
Define the following:
A consequence of the above is that these all have Hausdorff dimension .
and all have packing dimension 1.
and all have packing dimension .
Read more about this topic: Effective Dimension
Famous quotes containing the words comparison to, comparison, classical and/or dimension:
“In comparison to the French Revolution, the American Revolution has come to seem a parochial and rather dull event. This, despite the fact that the American Revolution was successful—realizing the purposes of the revolutionaries and establishing a durable political regime—while the French Revolution was a resounding failure, devouring its own children and leading to an imperial despotism, followed by an eventual restoration of the monarchy.”
—Irving Kristol (b. 1920)
“But the best read naturalist who lends an entire and devout attention to truth, will see that there remains much to learn of his relation to the world, and that it is not to be learned by any addition or subtraction or other comparison of known quantities, but is arrived at by untaught sallies of the spirit, by a continual self-recovery, and by entire humility.”
—Ralph Waldo Emerson (1803–1882)
“Et in Arcadia ego.
[I too am in Arcadia.]”
—Anonymous, Anonymous.
Tomb inscription, appearing in classical paintings by Guercino and Poussin, among others. The words probably mean that even the most ideal earthly lives are mortal. Arcadia, a mountainous region in the central Peloponnese, Greece, was the rustic abode of Pan, depicted in literature and art as a land of innocence and ease, and was the title of Sir Philip Sidney’s pastoral romance (1590)
“Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.”
—Tom Wolfe (b. 1931)