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In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets and is . The symmetric difference of the sets A and B is commonly denoted by (alternatively, ), , or .
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
Mutual information is a measure of the inherent dependence expressed in the joint distribution of and relative to the marginal distribution of and under the assumption of independence. Mutual information therefore measures dependence in the following sense: if and only if and are independent random variables.
The conditional mutual information is used to inductively define the interaction information, a generalization of mutual information, as follows: where. Because the conditional mutual information can be greater than or less than its unconditional counterpart, the interaction information can be positive, negative, or zero, which makes it hard to ...
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive). If , then (symmetric).
Less than or equal to the sum of individual entropies. The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity. This inequality is an equality if and only if and are statistically independent. [3] : 30.
A Young diagram or Young tableau, also called Ferrers diagram, is a finite collection of boxes, or cells, arranged in left-justified rows, with the row sizes weakly decreasing (each row has the same or shorter length than its predecessor). Young diagram. Listing the number of boxes in each row gives a partition of a positive integer n, the ...
English: Radially-symmetrical Five-set Venn Diagram devised by Branko Gruenbaum and rendered by CMG Lee to show the lowest common multiples of 2, 3, 4, ...
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