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Intuitively, the graph of a bounded function stays within a horizontal band, while the graph of an unbounded function does not. In mathematics , a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values is bounded .
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.
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 ...
A variety of templates and styles are available to create timelines. The {{Graphical timeline}} template allows representations of extensive timelines. The template offers complex formatting and labeling options to control the output. Typically, each use is made into its own template, and the template is then transcluded into the article.
In graph theory, a bound graph expresses which pairs of elements of some partially ordered set have an upper bound.Rigorously, any graph G is a bound graph if there exists a partial order ≤ on the vertices of G with the property that for any vertices u and v of G, uv is an edge of G if and only if u ≠ v and there is a vertex w such that u ≤ w and v ≤ w.
{{Graph, chart and plot templates | state = collapsed}} will show the template collapsed, i.e. hidden apart from its title bar. {{ Graph, chart and plot templates | state = autocollapse }} will show the template autocollapsed, i.e. if there is another collapsible item on the page (a navbox, sidebar , or table with the collapsible attribute ...
For a continuous function of a single variable, being of bounded variation means that the distance along the direction of the y-axis, neglecting the contribution of motion along x-axis, traveled by a point moving along the graph has a finite value.
The metric space (M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets of R n the two are equivalent. A metric space is compact if and only if it is complete and totally bounded. A subset of Euclidean space R n is compact if and only if it is closed and