Re: Questioning the defintions of set and element.

On May 1, 4:40 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On May 1, 1:00 pm, "porky_pig...@xxxxxxxxxxx" <porky_pig...@my-


But Mark is correct: both Wolfram and Wikipedia state [...]

It may be that those two sites corroborate one another in this
instance, and, of course, those sites are often correct on many
matters. My remark was general...In my opinion a good mathematical
vocabulary is not built by grabbing definitions ad hoc from such
sites, especially Wikipedia, which is nothing but ad hoc defintions
and formulations, written article-by-article (and edited by no single
responsible authority), without a systematic presentation among the
various articles on even one single branch of mathematics.

that the
'collection' is a common synonym for multiset. I looked at the
'multiset' definition on both Wolfram and Wiki sites but missed the
Wolfram definition of 'collection' as well as the fact that Wiki
redirects 'collection' to multiset. OK, mea culpa.

Though other people may have different experiences, it is my
impression that 'multiset' is a special notion in a way that
'collection' is not.

Well, my experience is that "collection" is used in the same way a
"family" is used: to informally distinguish the 'second level set' (an
aggregation of sets) from the "first level sets". So we say
"collection of open sets on interval [0,1]", for instance. In any
case, "collection" appears to be the term not reserved specifically
for anything. I can't argue with either Wiki or Wolfram that
"collection" is normally reserved for the synonym of "multiset" since
I haven't been dealing with multisets, don't have any textbooks which
deals with them - but I do have a number of textbooks that refer to
the "set of sets" as "collection of sets". Again, loose, informal
term. Frankly, I would rather *not* have "collection" as a standard
synonym for multiset since it only confuses the issue.
.

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