I have been trying to calculate it in several ways but I get stuck when it comes to many combinatorial issues... Like taking the number of possible relations and subtract the number different kinds of relations that do not meet the criteria. I could use some help...
2026-04-04 01:01:24.1775264484
How many partial order relations are there over N, the set of positive integers?
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HINT: How many permutations does $\Bbb N$ has? This alone gives you a lower bound, with a set of distinct linear orders, all isomorphic to the usual ordering of $\Bbb N$.