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  • https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/06%3A_Relations_and_Functions/6.04%3A_Ordering_Relations
    The prototype for ordering relations is ≤. Although a case could be made for using < as the prototypical ordering relation. These two relations differ in one important sense: ≤ is reflexive and ...The prototype for ordering relations is ≤. Although a case could be made for using < as the prototypical ordering relation. These two relations differ in one important sense: ≤ is reflexive and < is irreflexive. Various authors, having made different choices as to which of these is the more prototypical, have defined ordering relations in slightly different ways. The majority view seems to be that an ordering relation is reflexive (which means that ordering relations are modeled after ≤)
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/07%3A_Relations/7.04%3A_Partial_and_Total_Ordering
    Two special relations occur frequently in mathematics. Both have to do with some sort of ordering of the elements in a set. A branch of mathematics is devoted to their study. As you can tell from the ...Two special relations occur frequently in mathematics. Both have to do with some sort of ordering of the elements in a set. A branch of mathematics is devoted to their study. As you can tell from the brief discussion in this section, they cover many familiar concepts. A relation on a nonempty set A is called a partial ordering or a partial-order relation if it is reflexive, antisymmetric, and transitive. We often use ⪯ to denote a partial ordering, and called (A,⪯) a partially ordered set

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