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In mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram. Definition Let X {\displaystyle X} be a set with a partial order {\displaystyle \leq }. As usual, let < {\displaystyle <} be the relation on X {\displaystyle X} such that x < y {\displaystyle x<y} if and only if x y {\displaystyle x\leq y} and x y {\displaystyle x\neq y}. Let x {\displaystyle x} and y {\displaystyle y} be elements of X {\displaystyle X}. Then y {\displaystyle y} covers x {\displaystyle x}, written x y {\displaystyle x\lessdot y}, if x < y {\displaystyle x<y} and there is no element z {\displaystyle z} such that x < z < y {\displaystyle x<z<y}. Equivalently, y {\displaystyle y} covers x {\displaystyle x} if the interval [ x, y ] {\displaystyle [x, y]} is the two-element set { x, y } {\displaystyle \{x, y\}}. When x y {\displaystyle x\lessdot y}, it is said that y {\displaystyle y} is a cover of x {\displaystyle x}. Some authors also use the term cover to denote any such pair ( x, y ) {\displaystyle (x, y)} in the covering relation. Examples In a finite linearly ordered set {1, 2,..., n}, i + 1 covers i for all i between 1 and n 1 (and there are no other covering relations).
This GIF Bitmap Image Religion Coloring Pages HD Image Free is a part of Coloring Religion Category in Coloring Folder. Religion Coloring Pages HD Image Free has a Resolution of 571x787 Pixels. Religion Coloring Pages HD Image Free is of .gif (Graphics Interchange Format) Format. It's Size is 11.6KB. This GIF has been Downloaded 90 times till now. Religion Coloring Pages HD Image Free was Added on 07-07-2021. Download Religion Coloring Pages HD Image Free by clicking the button below:
Image Name: Religion Coloring Pages HD Image Free
Image Category: Coloring / Coloring Religion
Date Added: 07-07-2021
Resolution: 571x787
Format: GIF
Downloads: 90
Views: 168
Size: 11.6KB