Set up a Cartesian plane. On a sheet of paper mark two axes that cross at right angles - done. Excellent, except that paper and pencil aren't perfect.
If you successively fold a sheet of paper in half, it becomes impossible after 6 or 7 foldings (even if you start with something as large a sheet of a newspaper or as thin as tissue). Also, you can't draw a perfect line with a pencil as that line will always have a measurable width. That goes for points too.
There cannot exist a single point; it will always be a dot. And all dots will have a measurable diameter. Geometrically, circles may only have six neighbors, no matter how small you make them. It's only at the infinite limit that a discontinuity arises and you suddenly find that a point may be in contact with an infinite number of surrounding neighbors.
