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

From: <pamelafluente_at_libero.it>
Date: 26 Sep 2006 09:28:36 -0700

vc ha scritto:
> > Ah finally. That's just wanted you to get aware of:
> > You say:
> >
> > m(X) : [100, 1000],
> >
> > therefore log(m(X)) is formally the same as log( [100, 1000] )
> >
> > what does log( [100, 1000] ) means ?
>
> It means what it has always meant in the elementary school: mapping
> every point in the closed interval to its logarithm.

If you take log(S) as a shorthand for the set of point { Log(x), with x in S } , you
have proven that invariance does not hold for internal point. Just because
the mapping, altought monotonic, and hence "order preserving", is not linear.

"mapping every point in the closed interval to its logarithm"

If you take for instance (100 + 1000) / 2 and you map to its logaritm you do not have an "invariant" point.

That was my discussion point, and actually you proved it on the first place.

>

> > I just note that MEDIAN() is used by every DBA or user and they need
> > to
> > know nothing about probability measure.

The median of a finite set of number is defined elementarily, with no  need to introduce the concept of probability. It can be *also* defined within the
probability theory, but I *guess* it's not necessary (?) for most dbms (actually
I do not know about that, the people here should know something .... )

>
> That's funny, what do those hypothetical DBA/users use the median for
> if they, according to you, have no clue what the beast is ? Is it,
> like, religious ritual ?
>
> >
> > > >Of course any set of distinct values can be seen as a uniform discrete
> > > > distribution, but that is not necessary.
> > >
> > > That statement does not make any obvious sense.
> >
> > It does to me. {1 2 5} can be seen as a uniform with masses equal to
> > 1/3.
>
> How do you know ? Are you saying that three samples are sufficient to
> draw a conclusion like that ? If so, it would be quite a revolution
> in statistics, they do not need ridiculous stuff like the law of large
> numbers and such any more.

Forget about inference. I am talking of a discrete rv X which has a support made of
3 points. I am not doing inference based on a sample. (By the way the word
is sample not "samples" and what is in an observed sample are the observed values.
Occasionally I heard talking about samples, perhaps in medicine or experiments ? ...)

I do not understand why you insist with inference. Nobody talked about statistical
inference. We are discussing in a completely "descriptive" perspective (as opposite as
to "inferential") the concept of median of a finite set of numbers.

There is no sampling theory involved here.

-P

>
>
> >
> > Here again our opinions are not coincident.
> >
> >
> >
> > Thanks for the instructive discussion :)
> >
> > -P
Received on Tue Sep 26 2006 - 11:28:36 CDT

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