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...
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AGI
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