Re: Questioning the defintions of set and element.

On May 1, 5:12 pm, "Mark" <u...@xxxxxxxx> wrote:
<porky_pig...@xxxxxxxxxxx> wrote in message

news:26e692f7-e033-42fa-a78b-8fc5251c6e64@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx



On May 1, 3:42 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On May 1, 12:41 pm, "Mark" <u...@xxxxxxxx> wrote:

http://en.wikipedia.org/wiki/Collection_%28mathematics%29

You will immediately improve your mathematical vocabulary by ceasing
to rely on Wikipedia for it.

MoeBlee

But Mark is correct: both Wolfram and Wikipedia state 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.

And yet, once again, the fact that 'collection' is a common synonym
for multiset does not mean more than saying that 'family' is a common
synonym for the aggregation of sets. Synonym is not a definition.
Neither sets not multisets are defined. OK, the multiset is
generalization of a set, but that does not make multiset more defined
than set, ditto for 'collection' understood as a synonym of multiset.

In fact, the only time I saw the word 'collection' is as a reference
to the 'second level aggregation' of sets, just like family. But then
I never read anything on multisets, so may be this is a common
convention. *Still* does not make it a definition.

You're taking things way too deep. I was just trying to pin down a good
description by removing the circular vocabulary.

Well, what people have been trying to tell you
is that the way mathematics has found (the only
way!) in order to remove the circularity is to
leave the set concept undefined.

If you are interested in a non-mathematical
description, there are much better places
than sci.math to ask for them. Now, you said earlier

I just wanted to check if the definition I gave
for collection is ok, or if it would run in to any
problems with relation to set theory.

Non-mathematical descriptions (of anything)
cannot run into problems of any kind in relation
to set theory (or any to other mathematical theory,
for that matter).

-- m
.

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