```Date: Feb 7, 2013 6:51 PM
Author: fom
Subject: Re: Matheology § 210

On 2/7/2013 10:42 AM, WM wrote:> On 7 Feb., 15:49, fom <fomJ...@nyms.net> wrote:>> On 2/7/2013 7:54 AM, WM wrote:>>>>> Once upon a time there used to be a logocal identity: The expression>>> "Set X is countable" used to be equivalent to "Set X can be listed".>>>> Incorrect.>> First learn, then understand, then judge. > >I did.  I took the time to tolerate your nonsense.During that time I learned how your behavior is motivatedby an agenda rather than any honest and sincererespect for mathematical investigations.  Understandingthat (with a little help from others) I judged itwas time to keep your nonsense honest.> Otherwise you appear silly.How one appears to a WMoron is irrelevant.>> 1.1  Definition   The cardinality of A is less than or equal to the> cardinality of B (notation: |A| ? |B|) if there is a one-to-one> mapping of A into B.Coming from you, a true definition of any kind is a breath offresh air -- except that this definition has nothing to dowith the logical priority of well-order over cardinality, or,for that matter, your inappropriate use of the word "list" andits derivatives in a context where it has no commonly understooduse.But, since you so conveniently chose Jech, note that hisdefinition of the class of alephs relies on the notionof a least ordinal for any given class of sets thatcannot be distinguished on the basis of your definition.The problem with what you tried to do, going back tobasics, can be found in Aristotle.  One can never provea definition.  But one can destroy a definition.  Thisis the epistemic nature of whichever equivalence underliesany definition.  Although Cantor, himself, never quiterecognized the logical priority of well-ordering in full,his definition of "cardinal number" is not the definitionof "cardinality" you gave.  That general definition ismeaningless beyond a classificatory role without acanonical representative to which a determinate sense of"number" is attached.  This is implicit in Cantor'sobservation that the objects of a set are abstractedto "units" as part of the abstraction from a set toits "cardinal number". Jech's version of set theorydoes not abstract to "units". It fixes specific ordinalnumbers as the alephs.
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