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From: zuhair on 13 Feb 2010 23:46
On Feb 12, 2:25 am, zuhair <zaljo...(a)gmail.com> wrote:
> On Feb 10, 11:31 pm, zuhair <zaljo...(a)gmail.com> wrote:


One can actually define a selection trial as a trial to pick up an
object.

Now the "outcome" of a selection trial is either *failure* if the
object is not selected, or it is *the selected object* if selection is
made.

A collective attempt can be defined as the whole of all selection
trials.

Now the *Collection status* of a collective attempt can be defined as
the Whole of *outcomes* of all selection trials of the collective
attempt.

So for example the collection status of a collective attempt in which
0 was successfully selected in a theory in which the universe of
discourse have only 0 and 1 in it would be : {0, failure}

Now membership of a set can be defined in the following manner

X e Y if and only if Y is the collection status of the collective
attempt in which Y was selected.

In this way for example the empty set would be in reality the
following

{failure, failure, failure,....}

but a member of a set is defined to be a *selected object*

So that's why the empty set is empty, while at the same time it is a
collection status of failures, it is empty because it doesn't have
objects successfully selected.

I think this terminology clarify matters more.

Zuhair

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