Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
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lexicographic space - translation to russian
математика
лексикографическое пространство
![Orderings of the 3-[[subset]]s of <math>\{1, \ldots, 6\},</math> represented as sets of red squares, increasing sequences (in blue), or by their [[indicator function]]s, converted in [[decimal notation]] (in grey). The grey numbers are also the rank of the subsets in all subsets of <math>\{1, \ldots, 6\},</math> numbered in colexicographical order, and starting from 0. The lexicographical (lex) and colexicographical (colex) orders are on the top and the corresponding reverse orders (rev) on the bottom<br>One passes from an order to its reverse order, either by reading bottom-up instead of up-bottom, or by exchanging red and white colors.](https://commons.wikimedia.org/wiki/Special:FilePath/Orderings; 6 choose 3.svg?width=200 "Orderings of the 3-[[subset]]s of <math>\{1, \ldots, 6\},</math> represented as sets of red squares, increasing sequences (in blue), or by their [[indicator function]]s, converted in [[decimal notation]] (in grey). The grey numbers are also the rank of the subsets in all subsets of <math>\{1, \ldots, 6\},</math> numbered in colexicographical order, and starting from 0. The lexicographical (lex) and colexicographical (colex) orders are on the top and the corresponding reverse orders (rev) on the bottom<br>One passes from an order to its reverse order, either by reading bottom-up instead of up-bottom, or by exchanging red and white colors.")
![inversion vectors]] (in red) of permutations in ''colex'' order are in ''revcolex'' order, and vice versa.](https://commons.wikimedia.org/wiki/Special:FilePath/Orderings; permutations 5-cycle.svg?width=200 "inversion vectors]] (in red) of permutations in ''colex'' order are in ''revcolex'' order, and vice versa.")
математика
лексикографическое упорядочение
![A right-handed three-dimensional [[Cartesian coordinate system]] used to indicate positions in space<!--(See diagram description for needed correction.)-->](https://commons.wikimedia.org/wiki/Special:FilePath/3D coordinate system.svg?width=200 "A right-handed three-dimensional [[Cartesian coordinate system]] used to indicate positions in space<!--(See diagram description for needed correction.)-->")
![[[Cartesian coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Coord XYZ.svg?width=200 "[[Cartesian coordinate system]]")
![[[Cylindrical coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Cylindrical Coordinates.svg?width=200 "[[Cylindrical coordinate system]]")
![[[Spherical coordinate system]]](https://commons.wikimedia.org/wiki/Special:FilePath/Spherical Coordinates (Colatitude, Longitude).svg?width=200 "[[Spherical coordinate system]]")
математика
трехмерное пространство
Definition
Wikipedia
In economics, lexicographic preferences or lexicographic orderings describe comparative preferences where an agent prefers any amount of one good (X) to any amount of another (Y). Specifically, if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is. Only when there is a tie between bundles with regard to the number of units of X will the agent start comparing the number of units of Y across bundles. Lexicographic preferences extend utility theory analogously to the way that nonstandard infinitesimals extend the real numbers. With lexicographic preferences, the utility of certain goods is infinitesimal in comparison to others.
