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In such a 2D diagram of a 3D coordinate system, the z-axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective. In any diagram or display, the orientation of the three axes, as a whole, is arbitrary.
In many branches of mathematics, the term map is used to mean a function, [5] [6] [7] sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc.
Later reviewers have called his figures a statistical diagram rather than a map, but Levasseur referred to it as a carte figurative, the common term then in use for any thematic map. He produced them as teaching aids, immediately recognizing the intuitive power of size as a visual variable: "It is impossible that the child is not struck by the ...
Cartesian diagram, a construction in category theory; Cartesian geometry, now more commonly called analytic geometry; Cartesian morphism, formalisation of pull-back operation in category theory; Cartesian oval, a curve; Cartesian product, a direct product of two sets; Cartesian product of graphs, a binary operation on graphs
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).
Cartesian product of the sets {x,y,z} and {1,2,3}In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. [1]
Kruskal–Szekeres diagram, illustrated for 2GM=1. The quadrants are the black hole interior (II), the white hole interior (IV) and the two exterior regions (I and III). The dotted 45° lines, which separate these four regions, are the event horizons. The darker hyperbolas which bound the top and bottom of the diagram are the physical ...
The first diagram makes clear that the power set is a graded poset.The second diagram has the same graded structure, but by making some edges longer than others, it emphasizes that the 4-dimensional cube is a combinatorial union of two 3-dimensional cubes, and that a tetrahedron (abstract 3-polytope) likewise merges two triangles (abstract 2-polytopes).