Re: Temporal database - no end date

"-CELKO-" <jcelko212_at_earthlink.net> wrote in news:1169322838.251008.326040_at_11g2000cwr.googlegroups.com:

> [Sets without characteristic functions] What are those sets?
>
> 1) Fractals in which you cannot determine if a point x is on the curve
> or not.

Look up the Mandelbrot set *definition*. Besides, how "determine if a point x is on the curve or not" is related to the notion of the characteristic function ?

>
> 2) A set defined by Collatz's "3n+1 conjecture". Start with an
> integer (n) run this procedure on it

Collatz conjecture talks about sequences, not sets. There is no "set defined by Collatz's "3n+1 conjecture"". Besides, there is a simple algorithm of generating the sequence which is a constructive definition of the sequence.

>
> WHILE (n <> 1)
> DO IF odd(n) THEN n := 3n+1 ELSE n:= n/2;

That's the sequence-generating function defined constructively as an algorithm. What's your point ?

> 3) Any set defined by Godel's proof that you will have true theorems in
> a system complex enough to model arithmetic which cannot be proven true
> within that system.

Oh that's just too lame ! "Godel's proof" talks about provability, not truth although it can be interpreted in terms of "truth" in the standard model of the natural numbers. Nowhere in the proof is there a reference to "set". Does "Bew" ring a bell ? Have you seen the proof ? Once more, for slow learners, Godel's first theorem does not use any set theory machinery.

>
> There are tons more of these things.

Still waiting for at least one ! But never you mind ... You can save everyone including your own self tons of time if you realize that the characteristic function and set membership are just two different ways of talking about basically the same thing: function/application <=> set/membership ( see stratified lambda-claculus for example).

But... How's all this nonsense related to your misguided ideas about time 'n space ?. Speaking of which, have you already experienced an epiphany about chronons per chance ? Maybe by looking at your digital watch and seeing one-second chronons merrily running by ?

Anyways I won't talk about fractals, Godel, cabbages and kings any more unless they are related to the subject, sorry.

Good luck ;) Received on Sat Jan 20 2007 - 22:31:54 CET