Re: Cantor Normal Form

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 11/20/04 

Date: Sat, 20 Nov 2004 08:08:02 +0000

mindy wrote:

> Hi guys,
> What is the Cantor Normal Form of ordinals? Why is it that the Cantor
> Normal form of w + w^2 + w^3 + w^4 + 2 = w^4 + 2?

'cos w + w^2 = w^2 =/= w^2 + w etc.

A simpler example: 1 + w is the order type of a singleton followed
by a simple infinite sequence, that is it looks like
*, *, *, .....
so it's a simple infinite sequence: 1 + w = w.
But w + 1 is the order type of a simple infinite seuqence followed
by a singleton: so
*, *, *, .... *
Not the same as w :-) 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
Quantcast