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Given a function f with domain D and a preordered set (K, ≤) as codomain, an element y of K is an upper bound of f if y ≥ f (x) for each x in D. The upper bound is called sharp if equality holds for at least one value of x. It indicates that the constraint is optimal, and thus cannot be further reduced without invalidating the inequality.
Note: x inputs are from 0-100 and y inputs are from 0-100; This template also takes a variety of other parameters: |color-#= The template can take a color input for each do that is color-dot number (The default color is red) (overrides color-even and color-odd) |legend-color= This template can take a legend input to add to the legend.
A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...
This graph draws one or more independent numeric data series as lines. The data must be stored on Commons' Data namespace or come from Wikidata Query Service. Template parameters Parameter Description Type Status Table type tabletype Specifies the type of the table data. "tab" (default) uses data namespace on commons, without the data: prefix. "query" sends request to wikidata query service ...
A logarithmic chart allows only positive values to be plotted. A square root scale chart cannot show negative values. x: the x-values as a comma-separated list, for dates and time see remark in xType and yType; y or y1, y2, …: the y-values for one or several data series, respectively. For pie charts y2 denotes the radius of the corresponding ...
In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is larger than or equal to the absolute value of any value of any of the functions in the family.
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
A -bounded class of graphs is polynomially -bounded if it has a -binding function () that grows at most polynomially as a function of . As every n {\displaystyle n} -vertex graph G {\displaystyle G} contains an independent set with cardinality at least n / χ ( G ) {\displaystyle n/\chi (G)} , all polynomially χ {\displaystyle \chi } -bounded ...