Re: Coming soon -- new proof checking software

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"Dan Christensen" <[EMAIL PROTECTED]> wrote in

> > > ...unions can be defined on the power set of any given set.
> > >
> > Huh? What do you mean?
> >
> > >
> > > It is quite easy using the subset axiom.
> > >
> > Please demonstrate.
> >
>
> Let p be the power set of s. Let x and y be elements of p. Then we can
> construct a subset of s, selecting those elements that are in both x and y.
> That subset would be an element of p and the union of x and y.
>

to illustrate :

s = {3, 5, 7, 9}
p = {{3}, {5}, {7}, {9}, *{3, 5}, {3, 7}, *{3, 9}, {5, 7}, {5, 9}, {7, 9},
          {3, 5, 7}, *{3, 5, 9}, {3, 7, 9}, {5, 7, 9}, {3, 5, 7, 9}}

x = {3, 5}
y = {3, 9}

union = {3, 5, 9}

Herc