IJ footnote

[Andrew Dinn]

Adam Lou Stephanides writes:

> > And note that Cantor's proof does rely on taking an *ordering* of some
> > collection with the first cardinality and showing that there are
> > ommissions in the ordering. The jump to assume that all the missing
> > elements are `between' the ones in the ordering (which Cantor does
> > make) is actually rather a large one (look at it real closely, because
> > it's the one that gets you from the rationals to the reals and that's
> > where the rot creeps in).

> I'm a little confused here.  How does Cantor's Diagonal Proof assume
> that all the missing elements are "between" the ones in the ordering?
> I don't see him making this assumption in his 1891 statement of the
> Diagonal Proof.

The proof makes no such assumption hence does not depend on it. But
your confusion is of your own making. What I said was that Cantor made
such an assumption. This is not particularly to single him out since
it was (and still is) a common assumption.


Andrew Dinn
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