Re: What's the good word?

On Jun 14, 3:21 pm, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <84d4e723-a28e-4896-8337-008ad0c8c...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Edward Green  <spamspamsp...@xxxxxxxxxxx> wrote:

If I have eight objects in slots labeled "1,2,...,8", then I say the
objects are "ordered".

If I have the same eight objects inserted in slots labeled "Tom,
Fred,....,Haggis,Horton", then I've imposed some order on them -- but
I have not implied any "ordering" relation as inherent in the
integers.  What, if anything, is the shorthand for this idea?

"Combinations" refers to selections in which order is
irrelevant. "Permutations" refers to selections in which order is
important.

Thanks... but I don't think that's exactly the answer I was seeking.
I was asking what we call mappings or labelings which don't happen to
be ordered. Maybe "labeling". :-)

On Jun 14, 4:39 pm, "Phil Holman" <piholmanc@yourservice> wrote:

"Edward Green" <spamspamsp...@xxxxxxxxxxx> wrote in message

news:84d4e723-a28e-4896-8337-008ad0c8c692@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

If I have eight objects in slots labeled "1,2,...,8", then I say the
objects are "ordered".

If I have the same eight objects inserted in slots labeled "Tom,
Fred,....,Haggis,Horton", then I've imposed some order on them -- but
I have not implied any "ordering" relation as inherent in the
integers. What, if anything, is the shorthand for this idea?

"Bijectively mapped to a second set of equal cardinality" doesn't seem
catchy.

Nominal or categorical.

Hmm... so instead of saying "consider an ordered set", I ought to say
"consider a nominal set" or "consider a categorical set"? Is that
about the right idiom? How about a "labeled" or "structured" set --
the latter implying the mapping is onto some structure, if no
necessarily ordering?

It occurs to me that the general idea is "function"; an ordered set is
one with a function into the integers. We could have a function into
a "name set", an "index set", a set of "properties", or anything at
all. Or maybe you will say a partially ordered set may not admit of
this description. It simply has a partial binary relation: a < b or a
</= b for some (a,b). So in general a "labeled" set S has maps on S,
SxS, SxSxS, ... , onto arbitrary image spaces.

Now that's uselessly abstract!
.

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