Context and question: The axiomatization of mathematics, on the model of Euclid's Elements, had reached new levels of rigour and breadth at the end of the 19th century, particularly in arithmetic, thanks to the axiom schema of Richard Dedekind and Charles Sanders Peirce, and geometry, thanks to David Hilbert. At the beginning of the 20th century, efforts to base mathematics on naive set theory suffered a setback due to Russell's paradox (on the set of all sets that do not belong to themselves). The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel. Zermelo–Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics. But they did not explicitly exclude the possibility of the existence of a set that belongs to itself. In his doctoral thesis of 1925, von Neumann demonstrated two techniques to exclude such sets—the axiom of foundation and the notion of class.
Who resolved the problem of adequate axiomatization of set theory?
Answer: Ernst Zermelo and Abraham Fraenkel
Context and question: Depopulation, deurbanisation, invasion, and movement of peoples, which had begun in Late Antiquity, continued in the Early Middle Ages. The barbarian invaders, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Eastern Roman Empire—came under the rule of the Caliphate, an Islamic empire, after conquest by Muhammad's successors. Although there were substantial changes in society and political structures, the break with Antiquity was not complete. The still-sizeable Byzantine Empire survived in the east and remained a major power. The empire's law code, the Code of Justinian, was rediscovered in Northern Italy in 1070 and became widely admired later in the Middle Ages. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during the later 8th and early 9th century. It covered much of Western Europe, but later succumbed to the pressures of internal civil wars combined with external invasions—Vikings from the north, Magyars from the east, and Saracens from the south.
In what century did the Caliphate conquer North Africa?
Answer: 7th
Context and question: Where Congress does not make great and sweeping delegations of its authority, the Supreme Court has been less stringent. One of the earliest cases involving the exact limits of non-delegation was Wayman v. Southard 23 U.S. (10 Wet.) 1, 42 (1825). Congress had delegated to the courts the power to prescribe judicial procedure; it was contended that Congress had thereby unconstitutionally clothed the judiciary with legislative powers. While Chief Justice John Marshall conceded that the determination of rules of procedure was a legislative function, he distinguished between "important" subjects and mere details. Marshall wrote that "a general provision may be made, and power given to those who are to act under such general provisions, to fill up the details."
Where has the Supreme Court been known to be more stringent towards Congress?
Answer:
unanswerable