Yes there are many orders of infinity, but they're not usually described as "beyond infinity", they're described as kinds of infinity...
On Wed, Feb 26, 2014 at 2:18 PM, YKY (Yan King Yin, 甄景贤) < [email protected]> wrote: > On Wed, Feb 26, 2014 at 5:41 AM, Mike Archbold <[email protected]>wrote: > >> I need to read how Georg Cantor "counted beyond infinity"! I needed a >> good laugh :) >> > > > PS: It's not just weird mathematicians who accept his argument... for > example, the cardinality of the natural numbers is ω (omega); what is the > cardinality of the set of functions from integers to integers? According > to set theory, it should be ω^ω (omega to the power omega). A lot of > mathematicians / computer scientists write expressions like these nowadays > without even thinking much. But you actually have to accept "numbers" > like ω + 1 ("infinity plus 1") and 2 ω ("2 times infinity"), and so on, to > get to ω^ω. > > It is a convenient tool for mathematicians to compare the "sizes" of > infinite objects. I'm not familiar with this subject, but I think only a > fraction of non-mainstream mathematicians deny the validity of such > infinite objects... > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org "In an insane world, the sane man must appear to be insane". -- Capt. James T. Kirk ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
