Re: Questioning the defintions of set and element.


"John O'Flaherty" <quiasmox@xxxxxxxxx> wrote in message
news:nlrj14976helcnlne7fnqavsrllvme3qa8@xxxxxxxxxx
On Thu, 1 May 2008 12:55:46 +0100, "Mark" <user@xxxxxxxx> wrote:

Hi, most definitions of element and set I have come across, say something
like,

An element is any object of our perception or of our thought.
A set is a collection of unique elements.

So whats a collection?
Wolfram says it's a multiset.
Wiki says it's a multiset.

So whats a multiset?
Wolfram says it's a set-like object.
Wiki says it's a generalization of a set.

This basically gives the following definitions.

A multiset is a collection of elements
A set is a multiset of unique elements.

So whats a collection?
Would this be a good definition of colletion,
A collection is any elements which have something in common.

Or could someone give a better definition?

What do you mean by "definition"? It would seem, from the other
answers, that a definition in mathematics is a statement about
something in terms of other mathematical entities. Since no
mathematical system can be all-encompassing, for any particular system
there must be a ground floor of mathematically undefined somethings.
In ordinary language, however, a definition is a statement about
something that describes it (informally), and may try to exclude other
things. You should be able to define terms in this sense. A set is a
grouping of elements - a notional grouping based on a common property
of the elements, which may be as trivial as that they were assigned to
the same set.

--
John

By definition, I mean a statement which descibes some concept or object.
The standard meaning of the word defintion.


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