Re: Questioning the defintions of set and element.


"Martin Wanvik" <martinw@xxxxxxxxxxxx> wrote in message
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"Martin Wanvik" <martinw@xxxxxxxxxxxx> wrote in
message
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mathforum.org...
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?
[...]

You might find the following wikipedia articles
helpful:

http://en.wikipedia.org/wiki/Naive_set_theory
http://en.wikipedia.org/wiki/Axiomatic_set_theory

-- Martin Wanvik

I've read the articles, but they do not define what a
collection is.

Then you missed my point, which probably wasn't as obvious as I though it
would be. I'll try to be clearer: Your definition above of a set isn't
really a definition at all, in the mathematical sense of the word. It is
simply an intuitive, non-formal description of what we consider a set to
be, the kind one usually employs when doing naive (or informal) set
theory. The rigorous, formal way of doing these things is referred to as
axiomatic set theory.

-- Martin Wanvik

They are definitions.
You are assuming more that what is actually there.



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