Does this interpretation satisfy the Incidence of Geometry I

Does this interpretation satisfy the Incidence of Geometry? Is it a model for Incidence of Geometry?

Intepretation #1:

Points: all the points that can be traced on a sheet of paper

Lines: all the horizontal and vertical lines that can be traced on the sheet of paper

\"On\": a point is on a line if the point is an element of the line

Solution

Yes, it satisfies the model of incedence of geometry. Considering only 2-D(sheet of paper can be treated as a plane), if can be said that for:

Points: A, B, C
• Lines: {A, B}, {A, C}, {B, C}
• Point lies on l if the letter belongs to the set l.

Further,
• Points: A, B, C, D
• Lines: {A, B}, {A, C}, {A, D}, {B, C}, {B, D}, {C, D}
• Point lies on l if the letter belongs to the set l.

And so for any point from the set of n points on the sheet of paper, the point is on the line if the point is an element of the line.