# Re: Idempotence and "Replication Insensitivity" are equivalent ?

Date: 24 Sep 2006 19:36:12 -0700

Message-ID: <1159151772.661132.88370_at_h48g2000cwc.googlegroups.com>

Chris Smith wrote:

> Brian Selzer <brian_at_selzer-software.com> wrote:

[..]

> > You wrote, "There are some sets, such as {0, 1}, where every value between 0

*> > and 1 (including both endpoints) is minimum."
**> >
**> > Unless 0 and 1 belong to some domain other than integers, whole numbers or
**> > real numbers, it is clear that 0 is the minimum value of the set {0, 1}. I
**> > don't know where you came up with the idea that both values are minimum.
**>
**> That statement was made, though, in the context of defining the median.
**> The definition put forth (I don't recall by whom) is that the median is
**> the number c such that the sum of the distances of each member of the
**> set from c is minimized. In that context, the statement makes sense.
**> When considering the set {0, 1}, any real number c from zero to one
**> minimizes the sum of distances of members of the set from from c.
*

The veracity of the statement depends on *what* the set represents and what kind of median is discussed. In various contexts, the median can be either 0 or 1 or both, or the entire [0,1] interval(or 0.5 depending on the accepted convention).