Infinite or Finite: Examining Line Segments

[cam875]

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.

 

[HallsofIvy]

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.

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]

so its geometrical length is still considered finite although its set is considered infinite?

 

[Tac-Tics]

so its geometrical length is still considered finite although its set is considered infinite?

Length is a specific kind of measure on a set.

http://en.wikipedia.org/wiki/Measure_(mathematics )

This is distinct from the cardinality of the set. The cardinality of informally referred to as the "size" of the set.

http://en.wikipedia.org/wiki/Cardinality