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Epigraph (mathematics)
In mathematics, the epigraph or supergraph of a function f : X \to \infty, \infty/math> valued in the extended real numbers \infty, \infty= \R \cup \ is the set, denoted by \operatorname f, of all points in the Cartesian product X \times \R lying on or above its graph. The strict epigraph \operatorname_S f is the set of points in X \times \R lying strictly above its graph. Importantly, although both the graph and epigraph of f consists of points in X \times \infty, \infty the epigraph consists of points in the subset X \times \R, which is not necessarily true of the graph of f. If the function takes \pm \infty as a value then \operatorname f will be a subset of its epigraph \operatorname f. For example, if f\left(x_0\right) = \infty then the point \left(x_0, f\left(x_0\right)\right) = \left(x_0, \infty\right) will belong to \operatorname f but not to \operatorname f. These two sets are nevertheless closely related because the graph can always be reconstructed from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epigraph (literature)
In literature, an epigraph is a phrase, quotation, or poem that is set at the beginning of a document, monograph or section thereof. The epigraph may serve as a preface to the work; as a summary; as a counter-example; or as a link from the work to a wider literary canon, with the purpose of either inviting comparison or enlisting a conventional context. A book may have an overall epigraphy that is part of the front matter, or one for each chapter. Examples * As the epigraph to '' The Sum of All Fears'', Tom Clancy quotes Winston Churchill in the context of thermonuclear war:Why, you may take the most gallant sailor, the most intrepid airman or the most audacious soldier, put them at a table together – what do you get? The sum of their fears. * The long quotation from Dante's '' Inferno'' that prefaces T. S. Eliot's " The Love Song of J. Alfred Prufrock" is part of a speech by one of the damned in Dante's Hell. * The epigraph to E. L. Doctorow's ''Ragtime'' quotes Scott Jopl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
