[FOM] RE: FOM Digest, Vol 5, Issue 15

Matt Insall montez at fidnet.com
Mon May 12 10:31:06 EDT 2003

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 

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 

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