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Terence Tao summed up the advantage of the hyperreal framework by noting that it allows one to rigorously manipulate things such as "the set of all small numbers", or to rigorously say things like "η 1 is smaller than anything that involves η 0 ", while greatly reducing epsilon management issues by automatically concealing many of the ...
Tao's father, Billy Tao, [a] was a Chinese paediatrician who was born in Shanghai and earned his medical degree from the University of Hong Kong in 1969. [12] Tao's mother, Grace Leong, [b] was born in Hong Kong; she received a first-class honours degree in mathematics and physics at the University of Hong Kong. [10]
In 2016, Terence Tao published a paper titled "Finite time blowup for an averaged three-dimensional Navier–Stokes equation", in which he formalizes the idea of a "supercriticality barrier" for the global regularity problem for the true Navier–Stokes equations, and claims that his method of proof hints at a possible route to establishing ...
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Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, by Lars Ahlfors [54] Complex Analysis, by Elias Stein [55] Functional Analysis: Introduction to Further Topics in Analysis, by Elias Stein [56] Analysis (2 volumes), by Terence Tao [57] [58] Analysis (3 volumes), by Herbert Amann, Joachim Escher [59 ...
Although additive combinatorics is a fairly new branch of combinatorics (in fact the term additive combinatorics was coined by Terence Tao and Van H. Vu in their book in 2012), a much older problem, the Cauchy–Davenport theorem, is one of the most fundamental results in this field.
Even in English, the deviations from the ideal Zipf's law become more apparent as one examines large collections of texts. Analysis of a corpus of 30,000 English texts showed that only about 15% of the texts in it have a good fit to Zipf's law. Slight changes in the definition of Zipf's law can increase this percentage up to close to 50%. [45]
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