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Towards Limit Computable Mathematics
Lecture Notes in Computer Science, 2002The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to ?20-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recursive functions, which is
Susumu Hayashi, Masahiro Nakata
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Limit-Computable Mathematics and Its Applications
Lecture Notes in Computer Science, 2002Limit-Computable Mathematics (LCM) is a fragment of classical mathematics in which classical principles are restricted so that the existence theorems are realized by limiting recursive functions. LCM is expected to be a right means for "Proof Animation," which was introduced by the first author. In the lecture, some mathematical foundations of LCM will
Susumu Hayashi, Yohji Akama
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Dynamic and interactive mathematics learning environments: the case of teaching the limit concept
Teaching Mathematics and Its Applications, 2012 This theoretical study is an attempt to explore the potential of the dynamic and interactive mathematics learning environments (DIMLE) in relation to the technological pedagogical content knowledge (TPACK) framework.
Martinović Dragana
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Descartes on the limited usefulness of mathematics
Synthese, 2017Descartes held that practicing mathematics was important for developing the mental faculties necessary for science and a virtuous life. Otherwise, he maintained that the proper uses of mathematics were extremely limited. This article discusses his reasons which include a theory of education, the metaphysics of matter, and a psychologistic theory of ...
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Mathematical modelling of test limits and guardbands
Quality and Reliability Engineering International, 2009AbstractTo gain market share on product performance, suppliers will routinely specify product datasheet (DS) performance to tighter than six sigma specifications. To maintain quality levels in this instance, the product must be 100% tested in production to screen out parts that are outside specification.
Sandra Healy +2 more
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Limits of Mathematics in Statistics
The American Statistician, 1954Statistics as a Profession In 1944-45 the American Statistical Association approached the latter problem in connection with the development of the National Roster of Scientific and Specialized Personnel. Jointly with the Institute of Mathematical Statistics, the Association took part in defining the profession of statistics. They defined a statistician
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Limits and Bounds – Boundaries in Mathematics
ACADEMIA. The magazine of the Polish Academy of Sciences, 2022On the one hand, mathematics draws inspiration from everyday life and has the ambition to model it through a precise logical system, while on the other, it contributes new, sometimes very abstract ideas which expand our imagination and broaden our understanding of the surrounding reality.
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Mathematical limit theorems for computational creativity
IBM Journal of Research and Development, 2019Creativity is the generation of an idea or artifact judged to be novel and high-quality by a knowledgeable social group, and is often said to be the pinnacle of intelligence. Several computational creativity systems of various designs are now being demonstrated and deployed.
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The Limitations of Mathematical Logic
2013Despite the limitations of Frege’s and Gentzen’s analysis of deduction, throughout the twentieth century mathematical logic has been extolled, and the importance of Aristotle’s logic downplayed. For example, Russell states that mathematical logic gives thought “wings. It has, in my opinion, introduced the same kind of advance into philosophy as Galileo
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