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The Ghost In The Machine wrote:
> MoeBlee wrote:
> > Oops, nevermind that question. Obviously, every set is partially
> > ordered by the subset relation on the set.
> >
> > MoeBlee
> >
>
> Every *power* set, maybe. But the reals wouldn't be able
> to be ordered that way.
I hope I'm not mistaken that Rupert is correct in saying that I was
correct: The subset relation on a set is a partial ordering of the set.
> Of course it's easy enough to total order the reals;
> if each real number r is defined by at least one Cauchy
> sequence of rational numbers, then another real number
> s can also be defined by another Cauchy sequence, and if
> it is the case that there exists an M and a rational
> d > 0 such that for every i,j > M, r_i > s_j + d, then r > s.
I hope I'm not mistaken that the standard ordering on the reals is a
total ordering of the reals.
MoeBlee
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