Re: Transfinite Ordinal Multiplication

[William Elliot]

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.

2 * omega_0 = omega_0 < omega_0 + omega_0 = omega_0 * 2

> 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|

> Why?
>
Ordinal exponentation.