Context and question: The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g., x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which , while .
What is the difference of quantum disjunction from classic?
Answer: can be true even when both of the disjuncts are false
Context and question: A year before Alfonso III "the Great" of Asturias death, three of Alfonso's sons rose in rebellion and forced him to abdicate, partitioning the kingdom among them. The eldest son, García, became king of León. The second son, Ordoño, reigned in Galicia, while the third, Fruela, received Asturias with Oviedo as his capital. Alfonso died in Zamora, probably in 910. His former realm would be reunited when first García died childless and León passed to Ordoño. He in turn died when his children were too young to ascend; Fruela became king of a reunited crown. His death the next year initiated a series of internecine struggles that led to unstable succession for over a century. It continued under that name[clarification needed] until incorporated into the Kingdom of Castile in 1230, after Ferdinand III became joint king of the two kingdoms. This was done to avoid dynastic feuds and to maintain the Christian Kingdoms strong enough to prevent complete Muslim take over of the Iberian Peninsula and to further the Reconquista of Iberia by Christian armies.
Who was the second son of Alfonso III and what did he become king of?
Answer: Ordoño, reigned in Galicia
Context and question: The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Évariste Galois, extending prior work of Paolo Ruffini and Joseph-Louis Lagrange, gave a criterion for the solvability of a particular polynomial equation in terms of the symmetry group of its roots (solutions). The elements of such a Galois group correspond to certain permutations of the roots. At first, Galois' ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation θn = 1 (1854) gives the first abstract definition of a finite group.
People were looking for polynomial equations under what number?
Answer:
unanswerable