Partly it depends on how you define infinity and what the context is. I know there exists more than one definition for infinity. I tend toward philosophy. Hegel had both a qualitative and quantitative infinity, but in both cases it was really what he called "spurious infinity." Real infinity was the thought itself you had of uncountable numbers. Still, I think it sounds very strange to say something like you are going to count past infinity.
On 2/25/14, 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 > RSS Feed: https://www.listbox.com/member/archive/rss/303/11943661-d9279dae > Modify Your Subscription: > https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- 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
