Re: Distinct linear orderings on Z

From: Allan C Cybulskie (allan.c.cybulskie_at_yahoo.ca)
Date: 03/22/05 

Date: Mon, 21 Mar 2005 20:10:09 -0500

"Dave Seaman" <dseaman@no.such.host> wrote in message
news:d1kspv$iv2$2@mailhub227.itcs.purdue.edu...
> On Sun, 20 Mar 2005 12:49:34 -0500, Allan C Cybulskie wrote:
> >> What is your definition? Is it a property of sets, or is
> >> it a property of ordered sets?
>
> > 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.

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

No.

  If your answer is "yes", it means that
> "number of elements" is a property of ordered sets. If your answer is
> "no", it means that "number of elements" is a property of sets.

Nope, it's a property of containers, which include boxes and bags. A set is
a container that holds generally non-physical elements.

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