Why can you not define a line as an infinate set of points?
An infinite set of points can be a microscopically small line segment. An infinite number of points does not mean an infinitely long line.
What is a portion of a line that includes two points and all of the collinear points between the two points?
The various subsets are: The empty set: nothing. A point: a position on the line with 0 dimensions. A line segment: a 1-dimensional finite subset such that, if x and y are any two points in the subset then so is mx + (1-m)y from any m in [0,1]. That is, all points between x and y are also in the set. A ray: a 1-dimensional subset such that one of the points x and…