Constructing Space Without Points: Agree/Disagree?

[Kiki]

For sake of argument, let me define a point as a mathematical entity that occupies no space. Then, how can one hypothetically construct space, through addition of points, when each point contributes no space? Because adding points together consists of merely adding nothing to nothing, the most basic unit of space cannot be a point.

Do you agree or disagree with this? Why?

 

[houlahound]

Points like lines and planes are mathematical concepts, they don't exist precisely in the physical world.

Points are an idealised thing.

You might also consider that a 1 foot long ruler is finite but has infinity points in its length.

 

[phinds]

For sake of argument, let me define a point as a mathematical entity that occupies no space. Then, how can one hypothetically construct space, through addition of points, when each point contributes no space? Because adding points together consists of merely adding nothing to nothing, the most basic unit of space cannot be a point.

Do you agree or disagree with this? Why?

You don't get to make your own defintions in physics, when you are using words that already have well specified definitions. Your definition is not incorrect, but should be "... that has no dimensions" not " ... that occupies no space". One does not "construct space though addition of points" so your question is based on a false premise. One constructs space by increasing at least one dimension.