Re: Questioning the defintions of set and element.


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:e1oj14p69s4p4a15r46t4qtgkhnis70ms5@xxxxxxxxxx
On Thu, 1 May 2008 14:09:47 +0100, "Mark" <user@xxxxxxxx> wrote:


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:k0fj14lbq30cmomiiaoc1f513b35bu53jr@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.

You found this definition where, exactly?

In formal set theory the notions of "is a set"
and "is an element of" are _undefined_.

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?




David C. Ullrich

From, "Discovering Modern Set Theory by Winfried Just, Martin Weese,
American Mathematical Society"
http://books.google.co.uk/books?id=x74azoKzb_MC&pg=PA1&lpg=PA1&dq=%22our+perception+or+of+our+thought%22&source=web&ots=EEHVpDqYX5&sig=Tg7he0U1spehvNQf89utd6oefhA&hl=en

"By a "set" we mean any collection M into a whole of definite, distinct
objects m (which are called the "elements" of M) of our perception or of
our
thought." - Cantor

It's a good thing that you included the fact that they cite Cantor for
this.

Do the authors say that this _is_ the definition of "set", or do they
just say that this is what Cantor's definition _was_? (That was
a long time ago...)



David C. Ullrich

No, they don't, but are there any newer definitions?
I havn't seen any.


.

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