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Infinite sequences and infinite series
1977It is customary to use expressions such as $${u_1} + {u_2} + \cdots + {u_n} + \cdots ,\;and\;\sum\limits_{n = 1}^\infty {{u_n}}$$ (9.1) to represent infinite series. The u i are called the terms of the series, and the quantities $${s_n} = {u_1} + {u_2} + \cdots + {u_n},\quad n = 1,2, \ldots ,$$ are called the partial sums of the series.
Murray H. Protter, Charles B. Morrey
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Infinite kernel learning via infinite and semi-infinite programming
Optimization Methods and Software, 2010As data become heterogeneous, multiple kernel learning methods may help to classify them. To overcome the drawback lying in its (multiple) finite choice, we propose a novel method of 'infinite' kernel combinations for learning problems with the help of infinite and semi-infinite optimizations. Looking at all the infinitesimally fine convex combinations
Ozour-Akyuz, S, Weber, G-W
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IEEE Computer Graphics and Applications, 2006
When it comes to creative technique, cover artist Rick Spix will sometimes have a plan in mind while other times implement a more improvised trial-and-error approach. Spix says that the Ultrafractal program lets him simply create art the way he wants to.
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When it comes to creative technique, cover artist Rick Spix will sometimes have a plan in mind while other times implement a more improvised trial-and-error approach. Spix says that the Ultrafractal program lets him simply create art the way he wants to.
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Infinite subscripts from infinite exponents
Journal of Symbolic Logic, 1984Definition. For ordinals α ≤ κ, = [X]α = {p ⊆ X ∣ ot (p) = α}. For α ≤, κ, κ a cardinal, holds iff for every partition F: [Κ]κ → A, there is an X ∈ [Κ]κ with F constant on [X]α. X is called homogeneous for F. When A = 2 the subscript is omitted.It has been known since the sixties that for finite exponents all such properties are equivalent, i.e., κ ...
Baumgartner, James E., Henle, James M.
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Mind, 2007
Consider the following process of epistemic justification: proposition E-0 is made probable by El, which in turn is made probable by E-2, which is made probable by E-3, and so on. Can this process go on indefinitely? Foundationalists, coherentists, and sceptics claim that it cannot.
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Consider the following process of epistemic justification: proposition E-0 is made probable by El, which in turn is made probable by E-2, which is made probable by E-3, and so on. Can this process go on indefinitely? Foundationalists, coherentists, and sceptics claim that it cannot.
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2015
Finding the limit of a sequence is generally a difficult task. Sometimes, just determining whether a sequence has a limit is tough. Consider the sequence (18) in Example 4.1, that is, let a n be the nth digit in the decimal expansion of \(\sqrt{2}\). We know that (a n ) does not have a limit.
Miklós Laczkovich, Vera T. Sós
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Finding the limit of a sequence is generally a difficult task. Sometimes, just determining whether a sequence has a limit is tough. Consider the sequence (18) in Example 4.1, that is, let a n be the nth digit in the decimal expansion of \(\sqrt{2}\). We know that (a n ) does not have a limit.
Miklós Laczkovich, Vera T. Sós
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Infinite Diversity in Infinite Combinations
Psychological Inquiry, 1992The basic argument of Fox's article is that prejudice is an inevitable consequence of natural selection. The article is interesting to read, covers a tremendous amount of territory in sociobiology, social cognition, and Star Trek lore, and raises some of the fundamental issues at the core of intergroup perceptions. Unfortunately, this effort has fallen
Craig Johnson, Brian Mullen
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Infinite Games for Infinite Teams
2020Infinite Games for Infinite Teams was published by and in response to the DARPAPolyplexus Citizen Incubator: “Inventing a Remote Culture to Deal with Pandemics”,and was done so with the intent of discussing the questions outlined below. How are global online narratives constructed and received in 2020?
Friedman, Daniel, Cordes, RJ
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Infinite perspectives on ‘Infinite Nature’
Trends in Ecology & Evolution, 2007View Large Image | Download PowerPoint SlideBruce Hull has produced a remarkable sole-authored book that canvases a vast array of perspectives on the environment. The central thesis of Infinite Nature is that we need to move away from what Hull calls ‘environmental fundamentalism’ toward a more pluralistic consideration of the wide range of ...
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