Definition talk:Net (Preordered Set)

The first definition apparently does not allow for a definition of net convergence; this is the only sensible reason to introduce nets. As it is not citing any reference, I would like to delete it (Wikipedia and Conway both insist on a directed set). The diagonal relation (also known as the identity mapping) is a preorder, but not a directed set. It is obvious that no notion of convergence can be attached to this relation. Feel free to discuss. --Lord_Farin 09:52, 20 January 2012 (EST)