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The '''line''' is a basic [[geometry|geometric]] [[shape]]. It is such an intuitive concept that most mathematicians think it escapes a formal, general definition. Other such intuitive concepts are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].

The '''line''' is a basic [[geometry|geometric]] [[shape]]. It is such an intuitive concept that most mathematicians think it escapes a formal, general definition. Other such intuitive concepts are the [[point]], the [[plane]], the [[set]], [[symmetry]], and [[infinity]].

Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius of curvature]], yet both these definitions have philosophical flaws as well.

Attempts at providing a rigorous, abstract definition usually face philosophical [[paradox]]es, such as [[Euclid]]'s contention that lines are objects with "breadthless length."  In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite [[radius]] of [[curvature]], yet both these definitions have philosophical flaws as well.

A line that can be drawn on paper is not actually a line, but a representation of a line.  Two points determine a line.  A line can be broken down into finite [[line segment]]s.

A line that can be drawn on paper is not actually a line, but a representation of a line.  Two points determine a line.  A line can be broken down into finite [[line segment]]s.