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A pair network consists of four components: the 'relational-graph,' the 'logical-graph,' the 'surface-graph' (R-, L-, S-graphs), and the two operations Sponsor and Erase. The R-graph is simply the set of all items in the pair network, i.e., the structure as a whole of all arcs, labels (R-signs), and operations between them. The S-graph consists ...
The erase–remove idiom cannot be used for containers that return const_iterator (e.g.: set) [6] std::remove and/or std::remove_if do not maintain elements that are removed (unlike std::partition, std::stable_partition). Thus, erase–remove can only be used with containers holding elements with full value semantics without incurring resource ...
The axiom of pairing is generally considered uncontroversial, and it or an equivalent appears in just about any axiomatization of set theory. Nevertheless, in the standard formulation of the Zermelo–Fraenkel set theory, the axiom of pairing follows from the axiom schema of replacement applied to any given set with two or more elements, and thus it is sometimes omitted.
Silver forcing (after Jack Howard Silver) is the set of all those partial functions from the natural numbers into {0, 1} whose domain is coinfinite; or equivalently the set of all pairs (A, p), where A is a subset of the natural numbers with infinite complement, and p is a function from A into a fixed 2-element set.
The containers are defined in headers named after the names of the containers, e.g. set is defined in header <set>.All containers satisfy the requirements of the Container concept, which means they have begin(), end(), size(), max_size(), empty(), and swap() methods.
In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates
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For instance two sets may be made disjoint by replacing each element by an ordered pair of the element and a binary value indicating whether it belongs to the first or second set. [13] For families of more than two sets, one may similarly replace each element by an ordered pair of the element and the index of the set that contains it.