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  2. Preorder - Wikipedia

    en.wikipedia.org/wiki/Preorder

    Both of these are special cases of a preorder: an antisymmetric preorder is a partial order, and a symmetric preorder is an equivalence relation. Moreover, a preorder on a set X {\displaystyle X} can equivalently be defined as an equivalence relation on X {\displaystyle X} , together with a partial order on the set of equivalence class.

  3. Order theory - Wikipedia

    en.wikipedia.org/wiki/Order_theory

    The disjoint union of two posets is another typical example of order construction, where the order is just the (disjoint) union of the original orders. Every partial order ≤ gives rise to a so-called strict order <, by defining a < b if a ≤ b and not b ≤ a. This transformation can be inverted by setting a ≤ b if a < b or a = b. The two ...

  4. Comparison of music streaming services - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_music...

    Partial Yes Yes 120 [23] 16 [24] 9.6 [25] Partial [r 4] Yes Yes Yes Yes 9 other [p 4] 2007 Yes Gaana: Yes Yes No No Yes 45 201 [27] Never disclosed [27] Global Yes Yes Yes Yes 2010-04 Limited [n 6] hoopla: Yes Yes No No Yes 5 2.5 US, Canada Yes Yes Yes Yes ChromeOS, Roku, AirPlay, Chromecast, 2010 Yes iHeartRadio: Yes (radio mode) Partial (Plus ...

  5. Specialization (pre)order - Wikipedia

    en.wikipedia.org/wiki/Specialization_(pre)order

    In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space.For most spaces that are considered in practice, namely for all those that satisfy the T 0 separation axiom, this preorder is even a partial order (called the specialization order).

  6. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    Conversely, a strict partial order < on may be converted to a non-strict partial order by adjoining all relationships of that form; that is, := < is a non-strict partial order. Thus, if ≤ {\displaystyle \leq } is a non-strict partial order, then the corresponding strict partial order < is the irreflexive kernel given by a < b if a ≤ b and a ...

  7. Prewellordering - Wikipedia

    en.wikipedia.org/wiki/Prewellordering

    Preorder (Quasiorder) Partial order Total preorder Total order Prewellordering Well-quasi-ordering Well-ordering Lattice Join-semilattice Meet-semilattice Strict partial order Strict weak order Strict total order Symmetric: Antisymmetric: Connected: Well-founded: Has joins: Has meets: Reflexive: Irreflexive: Asymmetric

  8. Comparison of online music lockers - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_online_music...

    Like Amazon, Google eventually negotiated licenses before launching scan-and-match. In 2018, Google announced a transition from Google Play Music to YouTube Music, [6] and in May, 2020, Google had created a transfer tool to migrate added albums, uploads, history, and playlists. [7] On October 22, 2020, Google Play Music was discontinued. [8]

  9. Weak ordering - Wikipedia

    en.wikipedia.org/wiki/Weak_ordering

    A total order is a total preorder which is antisymmetric, in other words, which is also a partial order. Total preorders are sometimes also called preference relations . The complement of a strict weak order is a total preorder, and vice versa, but it seems more natural to relate strict weak orders and total preorders in a way that preserves ...