At some point in your life you were explained how to understand the dimensions of a line, a point, a plane, and a n-dimensional object.
For me the first instance that comes to memory was in 7th grade in a inner city USA school district.
Getting to the point, my geometry teacher taught,
"a point has no length width or depth in any dimensions, if you take a string of points and line them up for "x" distance you have a line, the line has "x" length and zero height, when you stack the lines on top of each other for "y" distance you get a plane"
Meanwhile I'm experiencing cognitive dissonance, how can anything with zero length or width be stacked on top of itself and build itself into something with width of length?
I quit math.
Cut to a few years after high school, I'm deep in the math's.
I rationalized geometry with my own theory which didn't conflict with any of geometry or trigonometry.
I theorized that a point in space was infinitely small space in every dimension such that you can add them together to get a line, or add the lines to get a plane.
Now you can say that the line has infinitely small height approaching zero but not zero.
What really triggered me is a Linear Algebra professor at my school said that lines have zero height and didn't listen to my argument. . .
I don't know if my intuition is any better than hers . . . if I'm wrong, if she's wrong . . .
I would very much appreciate some advice on how to deal with these sorts of things.