```Date: Oct 5, 2017 7:49 PM
Author: Markus Klyver
Subject: Re: Dipshit Zelos Malum claims that ...

Den torsdag 5 oktober 2017 kl. 16:48:33 UTC+2 skrev Python:> Markus Klyver wrote:> > Den torsdag 5 oktober 2017 kl. 06:21:32 UTC+2 skrev Zelos Malum:> ...> >> They aren't equivalent because dedekinds cut requires that ALL> >> rational numbers are included in the partition, as that is waht> >> defines a fucking partition. How many times does this have to be said?> > > > This is not true, though. A Dedekind cut must  necessarily contain all> > elements but one of the elements of ?. Consider a cut with all rationals> > strictly less and strictly greater than 0. Then 0 isn't in the cut.> > No. The Dedekind Cut for 0 is {x|x<0},{x|x>=0}, 0 is in the cut.> This is the standard way to inject Q inside the set of cuts, the> cut associated to a rational q is {x|x<q},{x|x>=q}> > (Wikipedia:It is a partition of the rational numbers into two non-empty> sets A and B, such that all elements of A are less than all elements of> B, and A contains no greatest element.)I stand corrected. 0 will be in B. I was confused by Rudin's "Dedekind cuts", which aren't partitions of ?. Rudin does not have an upper cut, but his construction is of course equivalent.
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