Re: Dimension of sequences
- Posted by CChris <christian.cuvier at agric?lture.g?uv.fr> Sep 16, 2007
- 609 views
Derek Parnell wrote: > > > I must disagree with Chris here. > > A sequence doesn't have a 'dimension' in geometrical sense. A sequence is not > a geometric object. > Of course, but it is a data structure (a tree), and has a dimension as such. There are dimensions in many other aspects of maths than geometry. CChris > Why do you need to know the 'dimension' of a sequence? I mean if you knew that > a given sequence has a dimension of 'x', what would you use 'x' for? > > Are you asking the right question? > > > Fernando Bauer wrote: > > Then, suppose you have the following sequence: > > { > > {1,1,1}, > > {1}, > > {1,1,1} > > } > > > > If I can view this sequence as a representation of the letter "U", > > using your answer below, I can conclude that the dimension of this > > sequence is 1. > > This sequence has a length of 3 and a depth of 1, so in that sense it has two > dimensions I suppose - Length and Depth. It also has a content of 7 (the > number > of atoms in total) so maybe a sequence has three dimensions? It also has a > sub-sequence > of 3, so maybe a sequence has four dimensions - Length, Depth, Content, > Sub-sequence. > Each of these is independant of the other so they sort of qualify as > dimensions, > no? But then 'Content' is kinda like 'area' in concept so maybe it doesn't > count > after all. > > > > > > Trying to answer that question, others more basics and related to that > > > > arise > > > > to me (sorry if they are stupid!): > > > > > > > > What is the dimension of the circumference ? > > Exactly my point. The dimension of a sequence is a meaningless concept. What > are you really trying to know about the sequence? > > -- > Derek Parnell > Melbourne, Australia > Skype name: derek.j.parnell