The discussion explores the nature of line segments in terms of their mathematical properties, specifically addressing whether a line segment is considered infinite or finite based on its points and length. The scope includes conceptual and mathematical reasoning related to set theory and geometry.
Participants express differing views on the relationship between the infinite nature of the points in a line segment and its finite length, indicating that the discussion remains unresolved.
Limitations include the dependence on definitions of length and cardinality, as well as the distinction between measure and set size, which are not fully explored in the discussion.
Yes, as a set containing an "infinite" number of points, it is an infinite set. But that has nothing to do with its length if you were thinking of that as being finite.cam875 said:If you were to describe a line segment as the set where all of its infinite points were individual elements within the set than wouldn't the overall set which is the line segment also be considered infinite and not finite.
cam875 said:so its geometrical length is still considered finite although its set is considered infinite?