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:
“It is very important not to become hard. The artist must always have one skin too few in comparison to other people, so you feel the slightest wind.”
—Shusha Guppy (b. 1938)
“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)
“Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a classical front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.”
—Eric Gill (1882–1940)
“Authority is the spiritual dimension of power because it depends upon faith in a system of meaning that decrees the necessity of the hierarchical order and so provides for the unity of imperative control.”
—Shoshana Zuboff (b. 1951)