Family Π
Family Π is a group of New Testament manuscripts. Belonging to the Byzantine text-type, it is one of the textual families of this group. The name of the family, "Π" (pronounced in English as "pie"), is drawn from the symbol used for the Codex Petropolitanus. One of the most distinct of the Byzantine sub-groups, it is very old and the third largest. The oldest Byzantine manuscripts belong to this family.
Hermann von Soden designated this group by the symbol "Ka". According to him, its text is not purely Byzantine.
Codices and manuscripts
Soden included the following in this group of codices: Cyprius (K), Petropolitanus (Π), 72, 114, 116, 178, 265, 389, 1008, 1009, 1079, 1154, 1200, 1219, 1346, and 1398. Lake added to this group of manuscripts: 489, 537, 652, 775, 796, 904, 1478, 1500, 1546, 1561, 1781, 1816. Soden also associated Codex Alexandrinus with this group. Wisse lists about 150 witnesses of the family, but the majority of them belong to this family only in some parts of their text. The Peshitta, in the Gospels, represents this family.
Index set
In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of a set J, then J is an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.
Examples
, where f : J → S is the particular enumeration of S.
.
, the indicator function on r is the function 
given byThe set of all the 
functions is an uncountable set indexed by 
.
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set.
See also
References
Family (Spanish band)
Family was a cult band from Spain in the 1990s. Although initially unsuccessful, Family gradually acquired a fanbase and is now highly recognised in the Spanish underground pop scene. Their only album, Un Soplo en el Corazón has been praised for its poetic lyrics, inspired music and elegant artwork.
Family - Un Soplo en el Corazón (Tracklist)
1. La Noche Inventada (2:24)
2. Nadadora (2:57)
3. Como un Aviador (3:19)
4. En el Rascacielos (2:32)
5. El Bello Verano (2:19)
6. Portugal (2:10)
7. El Buen Vigía (2:05)
8. Viaje a los Sueños Polares (2:53)
9. Al Otro Lado (2:02)
10. Carlos Baila (2:49)
11. Yo TePerdí una Tarde de Abril (3:01)
12. Dame Estrellas O Limones (2:24)
13. El mapa (2:20)
14. Martín se ha ido para siempre (3:09)
Byzantine Empire
The Byzantine Empire, sometimes referred to as the Eastern Roman Empire, was the continuation of the Roman Empire in the East during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, originally founded as Byzantium). It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic, cultural, and military force in Europe. Both "Byzantine Empire" and "Eastern Roman Empire" are historiographical terms created after the end of the realm; its citizens continued to refer to their empire as the Roman Empire (Ancient Greek: Βασιλεία τῶν Ῥωμαίων, tr. Basileia tôn Rhōmaiōn; Latin: Imperium Romanum), or Romania (Ῥωμανία), and to themselves as "Romans".
Several events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West divided. Constantine I (r. 324–337) reorganised the empire, made Constantinople the new capital, and legalised Christianity. Under Theodosius I (r. 379–395), Christianity became the Empire's official state religion and other religious practices were proscribed. Finally, under the reign of Heraclius (r. 610–641), the Empire's military and administration were restructured and adopted Greek for official use instead of Latin. Thus, although the Roman state continued and Roman state traditions were maintained, modern historians distinguish Byzantium from ancient Rome insofar as it was centred on Constantinople, oriented towards Greek rather than Latin culture, and characterised by Orthodox Christianity.
Byzantine (disambiguation)
Byzantine usually refers to the Roman Empire during the Middle Ages.
Byzantine may also refer to:
Other uses of the word Byzantine
See also
Podcasts:
