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The Keynesian cross diagram includes an identity line to show states in which aggregate demand equals output. In a 2-dimensional Cartesian coordinate system, with x representing the abscissa and y the ordinate, the identity line [1] [2] or line of equality [3] is the y = x line. The line, sometimes called the 1:1 line, has a slope of 1. [4]
Then f : X → Y has a closed graph (and a sequentially closed graph) in X × Y = ℝ 2 but it is not continuous (since it has a discontinuity at x = 0). [4] Let X denote the real numbers ℝ with the usual Euclidean topology, let Y denote ℝ with the discrete topology, and let Id : X → Y be the identity map (i.e. Id(x) := x for every x ∈ X).
The graph formulation of the union-closed sets conjecture states that every finite non-empty graph contains two adjacent non-heavy vertices. It is automatically true when the graph contains an odd cycle , because the independent set of all heavy vertices cannot cover all the edges of the cycle.
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 ...
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
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.
graph of an inequality ("a relation" (not wikilinked)) y ≤ x + 5; x 2 + y 2 ≤ 1; graph of a curve; graph of a parametric equation x = cos t and y = sin t; same as (x,y) = (cos t, sin t) graph of a point in two-dimensional Euclidean space. graph of an ordered pair, or 2- tuple (looks like a point in a plane) graph of a data set, where x ...
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.