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An ordered pair of vertices, such as an edge in a directed graph. An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would ...
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
As readers may not be aware of the area of mathematics to which the symbol that they are looking for is related, the different meanings of a symbol are grouped in the section corresponding to their most common meaning. When the meaning depends on the syntax, a symbol may have different entries depending on the syntax.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Roughly speaking, each vertex represents a 3-jm symbol, the graph is converted to a digraph by assigning signs to the angular momentum quantum numbers j, the vertices are labelled with a handedness representing the order of the three j (of the three edges) in the 3-jm symbol, and the graph represents a sum over the product of all these numbers ...
y = x 3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square:
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The graph always lies above the x-axis, but becomes arbitrarily close to it for large negative x; thus, the x-axis is a horizontal asymptote. The equation d d x e x = e x {\displaystyle {\tfrac {d}{dx}}e^{x}=e^{x}} means that the slope of the tangent to the graph at each point is equal to its height (its y -coordinate) at that point.