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Assume that the combined system determined by two random variables and has joint entropy (,), that is, we need (,) bits of information on average to describe its exact state. Now if we first learn the value of X {\displaystyle X} , we have gained H ( X ) {\displaystyle \mathrm {H} (X)} bits of information.
A faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full and faithful functor is not necessarily isomorphic to C), and two morphisms f : X → Y and f′ : X′ → Y′ (with different domains/codomains) may map to the same morphism in D.
whenever x > y and y > z, then also x > z whenever x ≥ y and y ≥ z, then also x ≥ z whenever x = y and y = z, then also x = z. More examples of transitive relations: "is a subset of" (set inclusion, a relation on sets) "divides" (divisibility, a relation on natural numbers) "implies" (implication, symbolized by "⇒", a relation on ...
Given a set X, a relation R over X is a set of ordered pairs of elements from X, formally: R ⊆ { (x,y) | x, y ∈ X}. [2] [10] The statement (x,y) ∈ R reads "x is R-related to y" and is written in infix notation as xRy. [7] [8] The order of the elements is important; if x ≠ y then yRx can be true or false independently of xRy.
A misleading [1] Venn diagram showing additive, and subtractive relationships between various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y ...
S x: symptoms surgery (though deemed by some as inappropriate) S 1: first heart sound: S 2: second heart sound: S 3: third heart sound S 4: fourth heart sound S&O: salpingo-oophorectomy Sb: Scholar batch SAAG: serum–ascites albumin gradient SAB: staphylococcal bacteremia spontaneous abortion (that is, miscarriage) SAD: seasonal affective ...
A misleading [1] information diagram showing additive and subtractive relationships among Shannon's basic quantities of information for correlated variables and .The area contained by both circles is the joint entropy (,).
The relationship x precedes y is written x ≺ y. The relation x precedes or is equal to y is written x ≼ y. The relationship x succeeds (or follows) y is written x ≻ y. The relation x succeeds or is equal to y is written x ≽ y. [citation needed]