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High Quality Content by WIKIPEDIA articles! Wac?aw Franciszek Sierpi?skov (Russian: ?vatswaf fra??t?i??k ??r?p?i?sk?i) (March 14, 1882, Moscow ? October 21, 1969, Warsaw) was a Polish-Russian mathematician. He was known for outstanding contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions and topology. He published over 700 papers and 50 books. Three well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpi?ski problem. ... Read more

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The purpose of Cantor's theory is to distinguish between greater, and smaller infinities. To supply us with infinitely many infinities. But it turns out that Cantor's Theory has just one infinity.All the Cantorian infinities are equal to each other.All the distnict infinities, that are believed to be Cantorian, are Non-Cantorian.This tale is about these distinct infinities. ... Read more

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This digital document is a journal article from Behaviour Research and Therapy, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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The objectives of the present study were to examine the degree of co-existence of hallucinations and delusions in the nonclinical population. In addition, we wished to investigate the role of metacognitions in hallucinations and delusions. Finally, we explored the relative roles of positive and negative metacognitive beliefs in proneness to hallucinations and delusions. Three hundred and thirty-one nonclinical participants completed instruments assessing: hallucination-proneness (Launay-Slade Hallucinations Scale; LSHS), delusion-proneness (21-item version of the Peters et al. Delusions Inventory; PDI-21) and metacognitive beliefs (Meta-Cognitions Questionnaire; MCQ). Participants were successively grouped according to their scores on the LSHS and the PDI-21. Results revealed that hallucination-proneness was positively and significantly associated with delusion-proneness. Furthermore, hallucination-prone and delusion-prone participants scored significantly higher on some sub-scales of the MCQ compared to non-prone participants. Finally, multiple regression analysis revealed that positive and negative beliefs were good predictors of proneness towards hallucinations and delusions. ... Read more

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Experts from different fields argue that there are good reasons to believe in the existence of the soul as distinct from the physical body. What do we mean when we speak about the soul? What are the arguments for the existence of the soul as distinct from the physical body? Do animals have souls? What is the difference between the mind and the soul? "The Soul Hypothesis" brings together experts from philosophy, linguistics and science to discuss the validity of these questions in the modern world. They contend that there is an aspect of the nature of human beings that is not reducible to the matter that makes up our bodies. This perspective is part of a family of views traditionally classified in philosophy as substance dualism, and has something serious in common with the ubiquitous human belief in the soul. "The Soul Hypothesis" presents views from a range of sciences and the resulting big picture shows, more clearly than one author could with one area of expertise, that there is room for a soul hypothesis. ... Read more

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Since their appearance in the late 19th century, theCantor--Dedekind theory of real numbers and philosophy of thecontinuum have emerged as pillars of standard mathematical philosophy.On the other hand, this period also witnessed the emergence of avariety of alternative theories of real numbers and correspondingtheories of continua, as well as non-Archimedean geometry,non-standard analysis, and a number of important generalizations ofthe system of real numbers, some of which have been described asarithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with theideas of Cantor and Dedekind and their reception at the turn of thecentury, the papers in the present collection are either concernedwith or are contributions to, the latter groups of studies. All thecontributors are outstanding authorities in their respective fields,and the essays, which are directed to historians and philosophers ofmathematics as well as to mathematicians who are concerned with thefoundations of their subject, are preceded by a lengthy historicalintroduction. ... Read more

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The technical successes of modern science have obscured a deeper understanding of its place in human knowledge and in our value systems. For many, science belongs in a separate "compartment" from normal human experience, confined to the word of the laboratory. This can give rise to a dark, impersonal and inhuman image of science.In this collection, scientists and thinkers from a range of disciplines examine the relationship of scientific knowledge and practice to the wider dimension of human life and awareness. For some this appears as a dialogue between science and spirituality, for others an investigation into consciousness and the intelligent heart of the cosmos. Whether in physics, cosmology of biology, these essays explore the very nature of knowledge itself and the continuing role of human creativity, emphasizing the need for crossing disciplinary boundaries in our search for understanding.The contributions are based on papers given over 20 years at the annual "Mystics and Scientists" conferences in England. ... Read more