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. |