Re: Questioning the defintions of set and element.

Mark 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.

So said Cantor, but that was a long time ago.

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?

In one of the usual set theories, ZF, everything is a set including
elements. What a set is, is defined contextually by the axioms. There
is no nominal definition of set.

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