Is it reasonable to imagine that undimensioned points make up dimensioned lines and also planes?

Question

Hi
As defined in geometry, points have no dimension, but how may it be imagined such points with no length no width and no thickness make up lines having length or planes having length and width as for the sum of any quantity of zeros is zero anyway. Thank you

Answer 1

Maybe so , but only in imagination:

 

  Euclid' s definition of point is : an entity with no parts

 

    Line is a shortest distance between 2 points , and is an entity that has no width or height

    Plane has no height.

    Volume that has 3 dimension that any substance for existence has to have 3 dimension and occupy space.

 

    Then they go 2 defining edge of 2 volumes make a plane

 

     Edge of 2 planes make a line

     Edge of 2 lines make a point.

 

    Then, Descartes a scientist of 18th century brilliantly creates coordinate system that all points of a plane can be specified with 2 numbers which are the horizontal and vertical coordinates of that plane.

 

  In math there are some abstract notions like no part of a point should be accepted as premise, then it took 18 century that come up with a gesture that gives a sense for no point not to be a complete void.