Re: Relative Cardinality



Virgil wrote:

> > I do not ask for insidious reasons or for bigotry. But it is quite
> > obvious that only such real numbers can exist and obey the
> > order-axioms, which have at least one completely well-defined n-adic
> > representation.
>
>
> It may be "quite obvious" but it is also quite false. One never need
> compare more than two reals for size at any one time, and then one does
> not need the entire expansion but only enough to determine their order.

How would you know that X and Y differ only at the n-th digit unless
you could be sure that they agree at the first n-1 digits? How can you
be sure that they agree at the first n-1 digits, unless they are given?

Regards, WM

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