COunting approximate values

[Leonard Soicher]

Dear All,

On Mon, Nov 03, 2003 at 01:20:17PM +0000, Peter Cameron wrote:
[...]
> I am not arguing against using the value-count mechanism for describing
> lists of real numbers; this is just a compact way of giving the information
> which could be written out as a list. My proposal is that, if the values
> are rationals, then the counts are correct and may be fed into such
> functions as "number of distinct efficiency factors",  but if not, then
> such functions and others which depend on them should be "unknown".
> 

How do you propose to represent multiplicities of, say, distinct eigenvalues 
when we know the exact multiplicities, but only know approximations to the 
(not neccesarily rational) eigenvalues? Do we do something like 
(0.683, at 2),(0.683, at 3) which we were discussing yesterday to mean that 
an eigenvalue x approximated by 0.683 occurs with multiplicity 2
and an eigenvalue y also approximated by 0.683 but not equal to x
has multiplicity 3? 

[...]

Leonard