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Two sets [twelve-tone series], P and P ′ will be considered equivalent [equal] if and only if, for any p i,j of the first set and p ′ i ′,j ′ of the second set, for all is and js [order numbers and pitch class numbers], if i=i ′, then j=j ′. (= denotes numeral equality in the ordinary sense).
Shamans and their practices continue in some parts of the Philippines. [205] The art of constellation and cosmic reading and interpretation is a fundamental tradition among all Filipino ethnic groups, and the stars are used to interpret for communities to conduct farming, fishing, festivities, and other important activities.
Designed Arc. Ralph Harrington Doane and Antonio Toledo. Home of the Philippine Legislature, National Assembly of the Philippines, Commonwealth Congress and the Philippine Congress. Now houses the National Museum of Fine Arts: NMP Declaration No. 07-2016: 2016: National Museum of Natural History Building (Old Agriculture and Commerce; and DOT ...
The definition of equivalence relations implies that the equivalence classes form a partition of , meaning, that every element of the set belongs to exactly one equivalence class. The set of the equivalence classes is sometimes called the quotient set or the quotient space of S {\displaystyle S} by ∼ , {\displaystyle \,\sim \,,} and is ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
The Order of National Artists of the Philippines (Tagalog: Orden ng mga Pambansang Alagad ng Sining ng Pilipinas) is an order bestowed by the President of the Philippines on Philippine nationals who have made significant contributions to the development of Philippine art. Members of the order are known as National Artists.
A similar extensional definition is usually employed for relations: two relations are said to be equal if they have the same extensions. In set theory, the axiom of extensionality states that two sets are equal if and only if they contain the same elements.
Assuming the existence of an infinite set N consisting of all natural numbers and assuming the existence of the power set of any given set allows the definition of a sequence N, P(N), P(P(N)), P(P(P(N))), … of infinite sets where each set is the power set of the set preceding it. By Cantor's theorem, the cardinality of each set in this ...