How To Create My Own Classifieds?

How does an infinite number of lines create a plane?

• When talking about dimensions (eg 1d, 2d, etc), we can begin on the zeroth dimension: a single point. It has no length, height, width, depth, or whatever. However, an infinite number of these locations/points will create a line - a collection of points. Now, if an infinite number of these lines are stacked upon each other, it will eventually create a plane. Again, if an infinite number of these planes are stacked upon each other, it will create a three dimensional object. And so on and so forth. ^ upon reading that, how does it actually work? How can a single point in the zeroth dimension, having no proportions, create a line (one dimension, having length)? Any organism living in a one dimensional world would have two options - the ability to move right and left. However, to create a one dimensional world, you would need to take an infinite amount of zero dimensional worlds. But in a zeroth dimension, how does an organism living in it move? For the organism in the first dimension must have been able to move right and left in the zeroth dimension. I think it's easier to understand what I'm trying to say from another perspective. Say we have lines. If we take an infinite amount of lines, it should create a plane. But how could those lines create a plane if each of those lines only have length, and no height? A plane consists of height and length - a line has length, only. So shouldn't it be impossible for a line with no height, multiplied by infinity, to create height? If this is true, then this is to say that a single point of the zeroth dimension has height, width, and length. For an infinite number of these points create a line, and another infinite create another line. An infinite amount of points in an infinite amount of lines will create a plane, and an infinite amount of such planes will create a three dimensional object. So then it would have to be assumed that there are no different dimensions - for the zeroth dimension has the abilities of the first dimension, second dimension, and so on. Another thing - if each point in the zeroth dimension is a location, then in order to create a three dimensional object, the points would have to be placed in a three dimensional pattern. How can this be possible if the point in a zeroth dimension does not have the abilities to move in height, length, or width? Please answer.

• Answer:

  Your confusion lies in your definition of a line and a plane. Contrary to popular belief, a line IS NOT an infinite number of points. Yes, a line can represent an infinite number of points that happens to lie in a pattern, but the points don't make the line. Same with lines and planes...points, lines and planes are three separate geometrical identities. How is it possible to divide a plane by an infinite number to get a line of zero width? You don't. Another problem is that you need to understand the behaviour of infinite cardinality, that is the number of elements in a set. A line will represent a set of different points. By our understanding, we may say that there are infinite number of points on a line. What about an infinite number of lines on a plane? There's the same number of lines on a plane as points on a line. The concept of adding infinitesimals together to make a whole may seem absurd, but realize that you are dealing with infinite, and not finite numbers, or length or height or width.