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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: a post for entry "ordinal number"''
by ratboy on 2004-11-19 13:25:45 |
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| > if you look at the entry "ordering relation", then you will
> see that there two notions are defined:
>
> 1) the relation "<=" which enables a<=a
> 2) and the relation "<" which doesn't enable a<a
>
> since in this entry one opeates with notation "<", then it
> is indirectly assumed that a<a can't be, and thus your
> example
>
> > "x is a proper subset
> > of y".
>
> is not an example of the ordering "<", but of "<=".
The proper subsets of a set x are just those subsets of x distinct from x.
The subsets of {0} are 0 and {0}, so the only proper subset of {0} is 0. The sets in S are 0, {0} and {0,{0}}; of these, the only one that is a proper subset of {0} is 0. Thus, the set of sets in S that are proper subsets of {0} is {0} as claimed.
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