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, classical and/or dimension:
“When we reflect on our past sentiments and affections, our thought is a faithful mirror, and copies its objects truly; but the colours which it employs are faint and dull, in comparison of those in which our original perceptions were clothed.”
—David Hume (1711–1776)
“Classical art, in a word, stands for form; romantic art for content. The romantic artist expects people to ask, What has he got to say? The classical artist expects them to ask, How does he say it?”
—R.G. (Robin George)
“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.”
—Marcus Minucius Felix (2nd or 3rd cen. A.D.)