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In mathematics, semi-infinite objects are objects which are infinite or unbounded in some but not all possible ways. ==In ordered structures and Euclidean spaces== Generally, a semi-infinite set is bounded in one direction, and unbounded in another. For instance, the natural numbers are semi-infinite considered as a subset of the integers; similarly, the intervals and and their closed counterparts are semi-infinite subsets of . Half-spaces are sometimes described as semi-infinite regions. Semi-infinite regions occur frequently in the study of differential equations.〔Bateman, (Transverse seismic waves on the surface of a semi-infinite solid composed of heterogeneous material ), Bull. Amer. Math. Soc. Volume 34, Number 3 (1928), 343–348.〕〔Wolfram Demonstrations Project, (Heat Diffusion in a Semi-Infinite Region ) (accessed November 2010).〕 For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar. A semi-infinite integral is an improper integral over a semi-infinite interval. More generally, objects indexed or parametrised by semi-infinite sets may be described as semi-infinite.〔Cator, Pimentel, (A shape theorem and semi-infinite geodesics for the Hammersley model with random weights ), 2010.〕 Most forms of semi-infiniteness are boundedness properties, not cardinality or measure properties: semi-infinite sets are typically infinite in cardinality and measure. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Semi-infinite」の詳細全文を読む スポンサード リンク
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