Context and question: Von Neumann was the first to establish a rigorous mathematical framework for quantum mechanics, known as the Diracvon Neumann axioms, with his 1932 work Mathematical Foundations of Quantum Mechanics. After having completed the axiomatization of set theory, he began to confront the axiomatization of quantum mechanics. He realized, in 1926, that a state of a quantum system could be represented by a point in a (complex) Hilbert space that, in general, could be infinite-dimensional even for a single particle. In this formalism of quantum mechanics, observable quantities such as position or momentum are represented as linear operators acting on the Hilbert space associated with the quantum system.
What von Neumann work preceded the axiomatiztion of quatum mechanics?
Answer: axiomatization of set theory
Context and question: By September 2008, average U.S. housing prices had declined by over 20% from their mid-2006 peak. As prices declined, borrowers with adjustable-rate mortgages could not refinance to avoid the higher payments associated with rising interest rates and began to default. During 2007, lenders began foreclosure proceedings on nearly 1.3 million properties, a 79% increase over 2006. This increased to 2.3 million in 2008, an 81% increase vs. 2007. By August 2008, 9.2% of all U.S. mortgages outstanding were either delinquent or in foreclosure. By September 2009, this had risen to 14.4%.
How many foreclosure proceedings were initiated by lenders in 2007?
Answer: nearly 1.3 million
Context and question:
India: Due to concerns about pro-Tibet protests, the relay through New Delhi on April 17 was cut to just 2.3 km (less than 1.5 miles), which was shared amongst 70 runners. It concluded at the India Gate. The event was peaceful due to the public not being allowed at the relay. A total of five intended torchbearers -Kiran Bedi, Soha Ali Khan, Sachin Tendulkar, Bhaichung Bhutia and Sunil Gavaskar- withdrew from the event, citing "personal reasons", or, in Bhutia's case, explicitly wishing to "stand by the people of Tibet and their struggle" and protest against the PRC "crackdown" in Tibet. Indian national football captain, Baichung Bhutia refused to take part in the Indian leg of the torch relay, citing concerns over Tibet. Bhutia, who is Sikkimese, is the first athlete to refuse to run with the torch. Indian film star Aamir Khan states on his personal blog that the "Olympic Games do not belong to China" and confirms taking part in the torch relay "with a prayer in his heart for the people of Tibet, and ... for all people across the world who are victims of human rights violations". Rahul Gandhi, son of the Congress President Sonia Gandhi and scion of the Nehru-Gandhi family, also refused to carry the torch.
How long was the route in India in miles?
Answer:
1.5