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The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that, in the case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover ...
According to two-dimensionalism, any statement, for example "Water is H 2 O", is taken to express two distinct propositions, often referred to as a primary intension and a secondary intension, which together compose its meaning. [1] [2] The primary intension of a word or sentence is its sense, i.e., is the idea or method by which we find its ...
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.
Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov and colleagues at Google and published in 2013. Word2vec represents a word as a high-dimension vector of numbers which capture relationships between words
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
For example Euclidean spaces of dimension n, and more generally n-dimensional Riemannian manifolds, naturally have the structure of a metric measure space, equipped with the Lebesgue measure. Certain fractal metric spaces such as the Sierpiński gasket can be equipped with the α-dimensional Hausdorff measure where α is the Hausdorff dimension ...
The idea of this system was developed in 1637 in writings by Descartes and independently by Pierre de Fermat, although Fermat also worked in three dimensions, and did not publish the discovery. [1] Both authors used a single ( abscissa ) axis in their treatments, with the lengths of ordinates measured along lines not-necessarily-perpendicular ...
A different and incompatible definition is sometimes used for the diameter of a conic section. In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7]