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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 ...
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.
Definition [ edit ] A sigmoid function is a bounded , differentiable , real function that is defined for all real input values and has a non-negative derivative at each point [ 1 ] [ 2 ] and exactly one inflection point .
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 ...
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 ...
For a continuous function of several variables, the meaning of the definition is the same, except for the fact that the continuous path to be considered cannot be the whole graph of the given function (which is a hypersurface in this case), but can be every intersection of the graph itself with a hyperplane (in the case of functions of two ...
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.
A subset S of a metric space (M, d) is bounded if there exists r > 0 such that for all s and t in S, we have d(s, t) < r. 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.