[CST-2] T in C

[Adam Martin]

So, in that case... (with N = intersection, because Outlook won't let me
type alt-139 for the intersection symbol....)

With the minimum fixed point being the N{ S c S' | f(S) c S } why is the
chain:

f(0) c f(f(0)) c f(f(f(0))) ....

an approximation to the min. prefixed. point?

Surely the chain above is U{ S c S' | S c f(S) } - i.e. the max postfixed
point?

Sorry - this one has long confused me, but I never got around to going over
it a second time in supervisions!

Adam

----- Original Message -----
From: "Shu Yan Chan" <syc22@cam.ac.uk>
To: <cst-2@srcf.ucam.org>
Sent: Tuesday, June 05, 2001 10:02 PM
Subject: Re: [CST-2] T in C


> > Could someone give me a concise definition of:
>
> I will give it a try:
>
>
> x is a fixed point for a function f(x) if f(x) = x  (or the sets are of
> equal size)
>
> x is a pre fixed point for a function f(x) if  f(x) is a subset of x
> x is a post fixed point for a function f(x) if  x is a subset of f(x)
>
>
> > A fixed point?
> >
> > A least fixed point?
> >
> > A most fixed point?
> >
> >
> > I always kind of understood what he was on about, but I found I couldn't
> > neatly define those terms without just rephrasing the equations for them
> as
> > used in Tarski's theorem.
> >
> > Regards,
> > Adam
> >
> >
> >
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> >
> >
>
>
>
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