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Unformatted text preview: , the order on N is the usual order, and the order on S is . 5. A relation on a set S is called irreexive if for every x S , x 6 x . We call a relation a strict partial order if it is irreexive and transitive. Prove that a strict partial order is antisymmetric. 6. Let C [0 , 1] be the set of continuous real-valued functions on [0 , 1]. De-ne a relation on C [0 , 1] by f g if and only if Z 1 ( g-f )( x ) dx > . Show that is a strict partial order. 7. Let be a strict partial order on S . Dene a relation on S by x y if and only if x y or x = y . Show that is a partial order on S....
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- Spring '10