```Date: Feb 26, 2013 9:03 PM
Author: David Bernier
Subject: Re: Problems with Infinity?

On 02/26/2013 04:23 PM, Brian M. Scott wrote:> On Tue, 26 Feb 2013 14:39:33 -0500, Shmuel Metz> <spamtrap@library.lspace.org.invalid>  wrote in> <news:512d0f75\$10\$fuzhry+tra\$mr2ice@news.patriot.net>  in> rec.arts.sf.written,sci.math:>>> In<20130225b@crcomp.net>, on 02/26/2013>>     at 12:51 AM, Don Kuenz<garbage@crcomp.net>  said:>>>> Answering my own question, Cantor's conjectures concern>>> set theory and only tangentially touch on the infinities>>> of complex variables. Using beginner's language, Cantor>>> uses two sets to define two levels of infinity. One set,>>> Aleph-0, holds countable infinity. The other set,>>> Aleph-1, holds continuum infinity, which includes>>> Aleph-0, along with every possible arrangement of>>> Aleph-0.>>> No; Cantor's work on cardinality has nothing to do with>> Complex Analysis,>> Though there are results in complex analysis that depend on> the continuum hypothesis, e.g.>> <http://www.renyi.hu/~p_erdos/1964-04.pdf?utm_medium=referral&utm_source=t.co>.>> (Followups set.)>> BrianFor non-constant entire functions f, g: C -> C, say  f '<' g   when  (Mf)(r) = o( (Mg)(r) ), r in [0, oo),where for r in  [0, oo), (Mf)(r) = max_{|z| = r} |f(z)| andsimilarly for r in [0, oo), (Mg)(r) = max_{|z| = r} |g(z)|,'M' for maximal or maximal function.If f(z) = z^2 and g(z) = z^3, (Mf) (r) = r^2, (Mg)(r) = r^3, andfor r>0, (Mf) (r) = (1/r)*(Mg)(r) , so (Mf)(r) is o( (Mg)(r) ),o being little-o notation.With the '<'  strict partial order,which ordinals can be embedded in (U, '<'), withU being the set of all entire functions and '<' thestrict partial order defined above?[ cf. wikipedia for non-crucialness of strict/non-strict: http://en.wikipedia.org/wiki/Partially_ordered_set#Strict_and_non-strict_partial_orders ].David Bernier-- dracut:/# lvm vgcfgrestoreFile descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh   Please specify a *single* volume group to restore.
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