Re: Distinct linear orderings on Z

From: Dave Seaman (dseaman_at_no.such.host)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 01:58:09 +0000 (UTC)

On Mon, 21 Mar 2005 20:10:09 -0500, Allan C Cybulskie wrote:

> "Dave Seaman" <dseaman@no.such.host> wrote in message
> news:d1kspv$iv2$2@mailhub227.itcs.purdue.edu...

>> > I think it would be properly called a property of containers, of which
> sets
>> > can be considered to be one of.

>> Ok, so a set is an example of a container. Is an ordered set also an
>> example of a container? If so, then you have simply evaded my question.

> Yes, as it inherits it from set. This is not an evasion since containers
> are a higher grouping and include things like real-world boxes.

What I was asking was whether an order is required before we can ask
about the number of elements in a set. The opinions seem to be divided
in this thread, with some claiming that an order is essential and others
denying it.

>> I'll ask it another way. Does changing the order of a set change the
>> "number of elements" in the set?

> No.

That puts you in the latter camp.

Order certainly does not make a difference in the cardinality. Whether it
makes a difference in the "number of elements" depends on how you define that
term. There seems to be no good definition. 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
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