Re: Temporal database - no end date
From: NENASHI, Tegiri <tnmail42_at_gmail.com>
Date: Sat, 20 Jan 2007 04:52:38 +0100 (CET)
Message-ID: <Xns98BDE8EA776CAasdgba_at_194.177.96.26>
>
> 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.
These view time, among other things, as discrete, dense, or continuous. Intuitively, discrete models of time are isomorphic to the natural numbers, i.e., there is the notion that every moment of time has a unique successor. Dense models of time are isomorphic to (either) the real or rational numbers: between any two moments of time there is always another. Continuous models of time are isomorphic to the real numbers, i.e., both dense and also, unlike the rational numbers, with no \gaps."
Date: Sat, 20 Jan 2007 04:52:38 +0100 (CET)
Message-ID: <Xns98BDE8EA776CAasdgba_at_194.177.96.26>
"Aloha Kakuikanu" <aloha.kakuikanu_at_yahoo.com> wrote in news:1169255697.528770.217910_at_m58g2000cwm.googlegroups.com:
>
> 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.
I am learning the chronons argot and I have found this:
##############################
These view time, among other things, as discrete, dense, or continuous. Intuitively, discrete models of time are isomorphic to the natural numbers, i.e., there is the notion that every moment of time has a unique successor. Dense models of time are isomorphic to (either) the real or rational numbers: between any two moments of time there is always another. Continuous models of time are isomorphic to the real numbers, i.e., both dense and also, unlike the rational numbers, with no \gaps."
#############################
(http://www.cs.aau.dk/~csj/Papers/Files/1992_jensenTSQL2status.pdf)
It is the mathematical education which is absent with the database researchers. How the dense model can be isomorphic to the real or rational numbers ? It is nonsense. It must be one or the other. So the argot is:
discrete -> natural numbers dense -> rational numbers or real numbers ???? continuous -> real numbers
-- TegiReceived on Sat Jan 20 2007 - 04:52:38 CET