A place where two or more things meet or overlap. Two lines or curves intersect at a point, two planes can intersect in a line, and so forth. The intersection of two or more sets , represented by , is the set of elements that all the sets have in common; in other words, all the elements contained in every one of the sets.
In plane geometry, an intersection is the crossing of two lines or curves at a point known as the point of intersection. In terms of analytic geometry, if two lines have equations y = f(x) and y = g(x) where f(x) and g(x) are functions of x, their points of intersection are given by those values of x for which f(x) = g(x). For example, the line y = 2x intersects the curve y = x2 in two points whose coordinates are given by solution of the equation 2x = x2; this has two roots, 0 and 2, and hence the points of intersection are (0,0) and (2,4). Should the equation f(x) = g(x) have roots that are not unique (i.e., two or more are equal), then the curves are tangential at the point or points defined by the equal roots.
Related category MATHEMATICAL TERMINOLOGY
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