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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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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 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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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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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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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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Mathematical moiré models and their limitations
Journal of Modern Optics, 2010In a previous recent paper we discussed the limitations of the Fourier-based model in the prediction of visible moire effects. Here, we extend the discussion to other mathematical models that are also being used in the moire theory: the classical indicial equations method for modelling the moire fringes between periodic or curvilinear gratings, and two
Amidror, Isaac, Hersch, Roger D.
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Limitations to Mathematical Knowledge
1982It is universally acknowledged that there are practical limitations to what we can compute, describe, communicate and prove. This paper is concerned with the possibility that there are limitations in principle . Some consequent restrictions on what can ever be known about the natural numbers are described, and there is a brief discussion of the ...
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The swap of integral and limit in constructive mathematics
Mathematical Logic Quarterly, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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