Re: Temporal database - no end date

Marshall wrote:
> On Jan 19, 2:41 pm, Larry Coon <lcnos..._at_assist.org> wrote:
> > Larry Coon wrote:
> > > No. Continuous means that there are no points between
> > > which there are other points. Dense implies discrete.
> > Fix to the above: Continuous means that there are no
> > two points between which there are NO other points.
>
> If I understand the terminology correctly, it is pretty weird.
> Apparently the rationals are continuous, but do not form
> a contiuum. The reals form a contiuum. The two terms
> are annoyingly close together.

http://en.wikipedia.org/wiki/Continuum_%28mathematics%29

I rephrase it as:

"The term the continuum sometimes is used as a sloppy reference to the real line.

It is defined by 2 conditions:

1. a continuum is a linearly ordered set that is "densely ordered",
i.e., between any two members there is another,
2. every non-empty subset with an upper bound has a least upper bound.

What I was saying is that condition #1 alone defines dense set, and not continuum. Received on Fri Jan 19 2007 - 19:14:57 CST