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Shapes that have reach infinity include a single point, a straight line, a full square, and; any convex set. The graph of ...
A vertex can reach a vertex (and is reachable from ) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with and ends with . In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
A set in the plane is a neighbourhood of a point if a small disc around is contained in . The small disc around p {\displaystyle p} is an open set U . {\displaystyle U.} In topology and related areas of mathematics , a neighbourhood (or neighborhood ) is one of the basic concepts in a topological space .
A term which shortcuts around calculation the mathematician perceives to be tedious or routine, accessible to any member of the audience with the necessary expertise in the field; Laplace used obvious (French: évident). complete intuition commonly reserved for jokes (puns on complete induction). diagram chasing
Define U to be open in X * iff the union of the equivalence classes that belong to U, is open as a subset of X. Then X * is a topological space with this topology - it is called the quotient space of X by the equivalence relation ~ (verify that this is a topological space, if you have not done so already).
The spider is 1 foot below the ceiling and horizontally centred on one 12′×12′ wall. The fly is 1 foot above the floor and horizontally centred on the opposite wall. The problem is to find the minimum distance the spider must crawl along the walls, ceiling and/or floor to reach the fly, which remains stationary. [1]
The term zenith sometimes means the highest point, way, or level reached by a celestial body on its daily apparent path around a given point of observation. [5] This sense of the word is often used to describe the position of the Sun ("The sun reached its zenith..."), but to an astronomer, the Sun does not have its own zenith and is at the ...