Re: Distinct linear orderings on Z

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 15:59:53 GMT

On Mon, 21 Mar 2005 21:14:11 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> in comp.ai.philosophy wrote:

>On Mon, 21 Mar 2005 20:37:59 GMT, Lester Zick wrote:
>> On Mon, 21 Mar 2005 17:50:25 +0000 (UTC), Dave Seaman
>
>> You might be interested in a collateral reply to Tony on this subject.
>> Cardinality in universal terms means exactly the same as number of
>> elements.
>
>A definition that works only for finite sets is not "universal".

And a definition that applies to all things is universal.

>> When cardinality is applied to undefined numbers of elements
>> the modern mathematical meaning of bijective mapping simply refers to
>> the slope or tangent of the set instead of the set itself, which is a
>> restricted parochial definition and not universal. In other words, the
>> modern math approach to set analysis in terms of cardinality is done
>> in non universal terms whereas the conventional interpretation of
>> cardinality in ordinary mathematics is universal in nature.
>
>Cardinality applies to arbitrary sets.

And what, exactly, is an arbitrary set?

> How do you compute the "tangent"
>of the set of all continuous mappings f: [0,1] -> R^n, to take an example
>that recently came up in sci.math? Or how about the "tangent" of the set
>of all subsets of R? I have quoted you the definition of cardinality,
>and it says nothing at all about "tangents".

How about the derivative?

>> Basically what I'm saying is that cardinality and number of elements
>> are identical concepts in universal terms of ordinary mathematics and
>> only become different when cardinality is interpreted in terms of
>> slopes or tangents as it is in bijective matching in set theory in
>> modern math. And of course it is this bifurcation between universal
>> and parochial applications of the single term, cardinality, that leads
>> directly to the nominally counterintuitive results in modern math.
>
>As best I can understand it, you are using "universal" to mean "applies
>only to finite sets", and "parochial" to mean "applies to all sets,
>whether finite or infinite". Huh?

Not quite. As I plainly state gauging infinities one to another by
means of tangents is a well established principle. Modern math is not
nearly so useful as ordinary math but considerably more complicated.

Regards - Lester

Relevant Pages

  • Re: Distinct linear orderings on Z
    ... I mean that cardinality means the ... It does indeed depend on bijections. ... Cardinality in universal terms means exactly the same as number of ... modern math approach to set analysis in terms of cardinality is done ...
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  • Re: Distinct linear orderings on Z
    ... > Cardinality in universal terms means exactly the same as number of ... > modern math approach to set analysis in terms of cardinality is done ... How do you compute the "tangent" ...
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  • Re: Distinct linear orderings on Z
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  • Re: Distinct linear orderings on Z
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  • Re: Distinct linear orderings on Z
    ... I've defined cardinality in universal terms as identical ... >> as more akin to tangentiality than cardinality in universal terms. ... properties such as set, ordinal, mapping, and bijection. ... with but which mathematikers pretend are defined in terms universal ...
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