The function f ( x), in set theory, defines a 'bijection' - a method of transformation between elements of two. Stover, Christopher and Weisstein, Eric W. As such, any one real number can be paired with any other in this manner, and only the points having coordinates ( x, f ( x)) for a deterministic, continuous f ( x) can be plotted along a line (this is what you learned in algebra). "The Linear Function and Its Reciprocal." Ch. 7 in AnĪtlas of Functions. "Triangle Centers and Central Triangles." Congr. Through Genius: The Great Theorems of Mathematics. Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections,Ĭontaining an Account of Its Most Recent Extensions, with Numerous Examples, 2ndĮd., rev. The line with x-intercept and y-intercept is given by the intercept Two lines lying in different planes that do not intersect one another Two lines lying in the same plane that do not intersect one another are said to be parallel A line may also be denoted with a single lower-case letterĮuclid defined a line as a "breadthless length," and a straight line as a line that "lies evenly with the points on itself" (Kline 1956, Dunham 1990).Ĭonsider first lines in a two-dimensional plane. Terminating at these points may be denoted. Similarly, the length of the finite line segment Harary (1994) called an edge of a graph a "line."Ī line is uniquely determined by two points, and the line passing through points and is denoted. While lines are intrinsically one-dimensional objects, they mayīe embedded in higher dimensional spaces. A line is sometimes called a straight line or, more archaically,Ī right line (Casey 1893), to emphasize that it has no "wiggles" anywhereĪlong its length. A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.
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