Squaring excellence and equality
نویسندگان
چکیده
منابع مشابه
Excellence and Equality in Education
I am very pleased to be able to participate in the inauguration of a new university, a new institution for the dissemination and development of knowledge old and new. This is the latest in a long list of similar organizations that, with their innovation and knowledge, have constituted a particularly important contribution to the Western world since the especially creative period that was the Mi...
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A set of natural numbers tiles the plane if a square-tiling of the plane exists using exactly one square of sidelength n for every n in the set. In [9] it is shown that N, the set of all natural numbers, tiles the plane. We answer here a number of questions from that paper. We show that there is a simple tiling of the plane (no nontrivial subset of squares forms a rectangle). We show that neith...
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We study the " approximate squaring " map f (x) := x⌈x⌉ and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then eventually an integer will be reached. We prove this when d = 2, and provide evidence that it is true in general by giving an upper bound on the density of the " exceptional set " of numbers which fail to reach an integer. We...
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متن کاملEquality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
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ژورنال
عنوان ژورنال: EMBO reports
سال: 2015
ISSN: 1469-221X,1469-3178
DOI: 10.15252/embr.201540931