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In metaphysics, identity (from Latin: identitas, "sameness") is the relation each thing bears only to itself. The notion of identity gives rise to many...

Black box Eubulides' second paradox Identity of indiscernibles List of fallacies Opaque context Transitivity of identity Use–mention distinction Metonymy...

a, one has a = a. Symmetry: for every a and b, if a = b, then b = a. Transitivity: for every a, b, and c, if a = b and b = c, then a = c. Substitution:...

concept Inscrutability of reference Masked-man fallacy Pure functions Referential transparency Transitivity of identity "Definition of "opaque context" |...

operation, and the symmetric closure of a relation R is its closure under this relation. Transitivity Transitivity is defined by the partial binary operation...

subset of Xn of tuples without repeated entries is transitive. For n = 2, 3 this is often called double, respectively triple, transitivity. The class of 2-transitive...

T\subseteq {\mathcal {C}}} . A strongly transitive class is automatically transitive. This strengthened transitivity assumption allows one to conclude, for...

jointly be used to define the equality relation. The symmetry and transitivity of equality follow from the first principle, whereas reflexivity follows...

insofar as ∅ is not an element of {{∅}}. Thus, in terms of failing the transitivity of identity, the search for true identity statements similarly fails....

or not may be a matter of definition (is every woman a sister of herself?), "is ancestor of" is transitive, while "is parent of" is not. Mathematical theorems...

but not zRx. Transitivity of incomparability for all x, y, z ∈ X, if x and y are incomparable with respect to R and if the same is true of y and z, then...

subset of a symmetric group that is closed under composition of permutations, contains the identity permutation, and contains the inverse permutation of each...

the identity function on X {\displaystyle X} .) R = R − 1 {\displaystyle R=R^{-1}} (symmetry). R R ⊆ R {\displaystyle RR\subseteq R} (transitivity). On...

form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. The...

operation, and has a multiplicative identity element. (Some authors define rings without requiring a multiplicative identity and instead call the structure...

However, it ultimately became an umbrella title for various directory-based identity-related services. A domain controller is a server running the Active Directory...

special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or...

commutative-transitive groups (or CT-groups for short) because commutativity is a transitive relation amongst the non-identity elements of a group if and...

specifically the "identity" and "predication" functions as pernicious but advocates the exclusion of all forms for the sake of simplicity. In the case of the "existence"...

diagram of a partial order is a drawing of the transitive reduction in which the orientation of every edge is shown by placing the starting vertex of the...