Show that if (P,<) and (Q, ) are isomorphic strictly ordered sets and < is a linear ordering, then is a linear ordering.
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we need to show that if then or . Let be an order isomorphism. As then , so or ( is linear). Therefore or , hence is linear.
Originally Posted by hammertime84 Show that if (P,<) and (Q, ) are isomorphic strictly ordered sets and < is a linear ordering, then is a linear ordering. What distinction does your text material make between linear ordering and strict ordering? Is it a matter of the reflexive property?
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