You're right of course that there's no need to invoke the ghost of Max Zorn to get maximal elements there!
22.
They make a more direct assumption that individual preferences have maximal elements, and examine conditions for the social preference to have a maximal element.
23.
They make a more direct assumption that individual preferences have maximal elements, and examine conditions for the social preference to have a maximal element.
24.
Of course, when the restriction of \ leq to S is a total order, the notions of maximal element and greatest element coincide.
25.
:I think you have confused maximal element with greatest element .-- talk ) 19 : 46, 20 February 2008 ( UTC)
26.
The extension theorem is then proved by showing that the set of strict partial orders containing " R " has some maximal element.
27.
Let m \ in S be a maximal element, for any s \ in S either s \ leq m or m \ leq s.
28.
In other words " H " is a maximal element of the partially ordered set of proper subgroups of " G ".
29.
This defines a partial order on decision rules; the maximal elements with respect to this order are called " admissible decision rules ."
30.
The third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank.
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