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For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two, etc. The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded .
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For example, the sentences "Pat loves Chris" and "Chris is loved by Pat" mean roughly the same thing and use similar words. Some linguists, Chomsky in particular, have tried to account for this similarity by positing that these two sentences are distinct surface forms that derive from a common (or very similar [1]) deep structure.
Created Date: 8/30/2012 4:52:52 PM
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
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In dimension 5, the smooth classification of simply connected manifolds is governed by classical algebraic topology. Namely, two simply connected, smooth 5-manifolds are diffeomorphic if and only if there exists an isomorphism of their second homology groups with integer coefficients, preserving the linking form and the second Stiefel–Whitney ...