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Ok. But I still don't agree that the property of antisymmetry implies or requires that restriction.
by ajarmst 6y ago
Ok. But I still don't agree that the property of antisymmetry implies or requires that restriction.
- ajarmst 6y agoIf we agree that the axiom of extensionality applies, then the restriction of no ties is implied. I don't think antisymmetry is necessary or sufficient for it.
- BoiledCabbage 6y agoOk, how are you defining a tie? I believe the author is defining a tie as the following: (a <= b) && (b <= a) && (a != b) Then a and b are "tied". Where "!=" means a and b are different.
- ajarmst 6y agoI'm fine with that restriction. But that isn't the axiom of antisymmetry. That's the axiom of antisymmetry plus a rule that holds that equality implies identity (which would be typically described in terms of the axiom of extensionality). My problem is with the implied claim that antisymmetry alone gives you that restriction, which is incorrect. Antisymmetry is entirely consistent with collections that contain equal but distinct elements.