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The limit, should it exist, is a positive real solution of the equation y = x y. Thus, x = y 1/y. The limit defining the infinite exponential of x does not exist when x > e 1/e because the maximum of y 1/y is e 1/e. The limit also fails to exist when 0 < x < e −e. This may be extended to complex numbers z with the definition:
A correct evaluation order is a numbering : of the objects that form the nodes of the dependency graph so that the following equation holds: () < (,) with ,. This means, if the numbering orders two elements a {\displaystyle a} and b {\displaystyle b} so that a {\displaystyle a} will be evaluated before b {\displaystyle b} , then a ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations. [1]
A three-dimensional graph may refer to A graph (discrete mathematics), embedded into a three-dimensional space;
The formula was defined by Jeff Tupper and appears as an example in Tupper's 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms. [1] This paper discusses methods related to the GrafEq formula-graphing program developed by Tupper. [2] Although the formula is called "self-referential", Tupper did not name it as such. [3]
If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1273 ahead. Let's start with a few hints.
Powers of graphs are referred to using terminology similar to that of exponentiation of numbers: G 2 is called the square of G, G 3 is called the cube of G, etc. [1] Graph powers should be distinguished from the products of a graph with itself, which (unlike powers) generally have many more vertices than the original graph.