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On Mon, 2003-03-17 at 07:13, Igor Pechtchanski wrote: > > And for clarity: my suggested tweak is also not sufficient to provide a > > weak ordering. > > Rob > > Rob, > > Your suggested tweak provides a total ordering. The "unordered(x,y)" > [!(x < y) && !(y < x)] relation is false for any x != y [since either > (x < y) or (y < x) always holds]. For my example, yes. The problem is when you introduce z. > So all equivalence classes have one > element: "unordered(x,x)" is always true. You get transitivity trivially, > as "unordered(x,y) && unordered(y,z)" is only true if x == y == z, and > then you also have "unordered(x,z)". But: we break the ordering transitivity. > Transitivity > x < y and y < z implies x < z [3] y:= foo: gam x:= gam z:= bar: foo both our operators give x < y && y < z && !x < z (dep) (dep) (alpha) which isn't transitive. Rob -- GPG key available at: <http://users.bigpond.net.au/robertc/keys.txt>.
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