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2. Antichain - Wikipedia

   en.wikipedia.org/wiki/Antichain

   Any antichain can intersect any chain in at most one element, so, if we can partition the elements of an order into chains then the width of the order must be at most (if the antichain has more than elements, by the pigeonhole principle, there would be 2 of its elements belonging to the same chain, a contradiction).

3. Dilworth's theorem - Wikipedia

   en.wikipedia.org/wiki/Dilworth's_theorem

   An antichain in a partially ordered set is a set of elements no two of which are comparable to each other, and a chain is a set of elements every two of which are comparable. A chain decomposition is a partition of the elements of the order into disjoint chains. Dilworth's theorem states that, in any finite partially ordered set, the largest ...

4. Hausdorff maximal principle - Wikipedia

   en.wikipedia.org/wiki/Hausdorff_maximal_principle

   In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset, where "maximal" is with respect to set inclusion.

5. Ichthyosauria - Wikipedia

   en.wikipedia.org/wiki/Ichthyosauria

   Many of these genera possessed streamlined, dolphin-like thunniform bodies, although more basal clades like Eurhinosauria, which include Leptonectes and Eurhinosaurus, had longer bodies and long snouts. Few ichthyosaur fossils are known from the Middle Jurassic. This might be a result of the poor fossil record in general of this epoch. The ...

6. AOL Mail

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   Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

7. Which landmarks are affected by the wildfires in Los Angeles ...

   www.aol.com/landmarks-affected-wildfires-los...

   The Getty Villa art museum is threatened by the flames of the wind-driven Palisades Fire in Pacific Palisades, California, Jan. 7, 2025. A fast-moving brushfire in a Los Angeles suburb burned ...

8. False killer whale - Wikipedia

   en.wikipedia.org/wiki/False_killer_whale

   The false killer whale reaches a maximum length of 6 m (20 ft), though size can vary around the world. It is highly sociable, known to form pods of up to 50 members, and can also form pods with other dolphin species, such as the common bottlenose dolphin (Tursiops truncatus). It can form close bonds with other species, as well as have sexual ...

9. Smartwatch and fitness tracker bands have elevated levels of ...

   www.aol.com/lifestyle/smartwatch-fitness-tracker...

   “A significant fraction of short-chain PFAS deposited on the skin can migrate into the dermis, and some fraction will actually enter the bloodstream after passing through our skin,” Peaslee says.