[FOM] RE: FOM Digest, Vol 5, Issue 15
Matt Insall
montez at fidnet.com
Mon May 12 10:31:06 EDT 2003
Slater:
John Pais (FOM Digest Vol 5 Issue 14) objects to my pointing out
that, unlike rational numbers, Dedekind cuts have complements, and
equivalence classes of Cauchy sequences of rational numbers have
members:
Insall:
I will not object to your pointing things out,
but I would like to point something out. In one
currently common presentation of the rational
numbers in advanced courses, the rational numbers
also have complements in the sense in which Dedekind
Cuts have complements. But if one uses the approach
I recently described - namely the use of urelements -
then the real numbers in such a model do not have
complements, while the Dedekind cuts still do have
complements.
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