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William Elliot wrote:
> On Sun, 30 Apr 2006, zuhair wrote:
>
> > It says that Trasnfinite Ordinal multiplication is non commutative.
> >
> > 2*Omega is different from Omega * 2
> >
> > so 2+2+2+............. = Omega
> >
> > While Omega + Omega = 2.Omega>Omega
> >
> No. Multiplication isn't communative.
What are you saying is exactly what I am saying. So why you are saying
no.
I am saying that number two summed by itself Omega times will only
result in Omega
While if Omega is summed with itself it will result in twice Omega
which is bigger than Omega.
>
> 2 * omega_0 = omega_0 < omega_0 + omega_0 = omega_0 * 2
You are only repeating what I am saying. But I think it is dot symbole
that confused you.
In Introduction to mathematical philosophy n.Omega means Omega summed
by itself n times, while Omeage.n means n summed by itself Omega times
OK.
so according to the notation present in that book.
for example 2+2+2+2+............ is writtin as Omega.2 = Omega
While Omega + Omega is writtin as 2.Omega which is bigger than Omega.
I hope that this resolved you confusion about what I said.
>
> > I see this a little bit fabricated! or let's say fixed.
>
> 2^omega_0 = omega_0 < omega_1 = aleph_1 <= |2|^aleph_0 = |2|^|omega_0|
I don't know weather you are right her or not.
>From what i know is that 2^Omega-0 > Omega-0
The exact relation between the cardinality of continuum 2^ aleph-0 and
aleph_1
is not known till now.
Zuhair
>
> > Why?
> >
> Ordinal exponentation.
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